ChemWiki - User contributions [en]

Rep:Mod:mhl12comp

2014-11-21T11:35:34Z

Mhl12: /* Optimization of Al2Cl2Br4 */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length that of terminal Al-halides bond indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|No
|Bend
|-
|90
|0
|No
|Bend
|-
|99
|3
|NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|57
|Yes
|Bend
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal halide; this is most probably due to the 3c-4e bonding.

The cis trans configuration does not affect the IR spectrum significantly. They both have similar stretches at similar frequencies with similar intensities. The reorder of modes does not manifest in this case is due to the fact that both the molecules have the same element in it. And the configuration of the molecules is very similar in a way that the bridging molecules remain to be Br, only changing the position of terminal halides.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:32:30Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|No
|Bend
|-
|90
|0
|No
|Bend
|-
|99
|3
|NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|57
|Yes
|Bend
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal halide; this is most probably due to the 3c-4e bonding.

The cis trans configuration does not affect the IR spectrum significantly. They both have similar stretches at similar frequencies with similar intensities. The reorder of modes does not manifest in this case is due to the fact that both the molecules have the same element in it. And the configuration of the molecules is very similar in a way that the bridging molecules remain to be Br, only changing the position of terminal halides.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:28:54Z

Mhl12: /* Frequency Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|No
|Bend
|-
|90
|0
|No
|Bend
|-
|99
|3
|NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|57
|Yes
|Bend
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal halide; this is most probably due to the 3c-4e bonding.

From spectra of isomer 3 and isomer 4, the cis trans configuration does not affect the IR spectrum significantly.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:24:43Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal halide; this is most probably due to the 3c-4e bonding.

From spectra of isomer 3 and isomer 4, the cis trans configuration does not affect the IR spectrum significantly.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:23:42Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal halide; this is most probably due to the 3c-4e bonding.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:23:21Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.

The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H. And chlorine vibrate more strongly than bromine, most probably due to their masses.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one. Bridging halides vibrate in a smaller amplitude than terminal amplitude; this is most probably due to the 3c-4e bonding.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:17:27Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

In the IR spectrum from above, for example in spectrum in isomer 1, for the same symmetrical stretching of Cl- Al, it can be due to vibrational movement of Cl or Al or both. They have different frequencies and intensities. The reordering of vibrational modes make it hard to analyse and we have to examine all vibrational movement one by one.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:08:29Z

Mhl12: /* Frequency Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Symmetric Bridging Cl Al stretch (Cl)
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Bend
|-
|400
|463
|Yes
|Symmetric Bridging Cl Al stretch (Al)
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|Ring breathing
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T11:00:31Z

Mhl12: /* Bond Energy */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: As this N->B a dative covalent bond, we are comparing N-B bond with normal type of covalent bond. C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:58:06Z

Mhl12: /* Frequency Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 0 minutes 50.0 seconds || 0 days 0 hours 2 minutes 22.4 seconds||0 days 0 hours 1 minutes 0.9 seconds ||0 days 0 hours 1 minutes 1.7 seconds.
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:54:48Z

Mhl12: /* Vibrational spectrum for NH3 */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

NH3 with C3V point group has relatively small number of IR active bands.

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:53:16Z

Mhl12: /* Vibrational Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

The frequency of A2" umbrella motion of BH3 and GaBr3 1163 and 100 respectively. The difference in frequencies has been explained above. Umbrella motion of BH3 is mode #1 with a high intensity (93), while umbrealla motion of GaBr3 is mode #3 with low intensity (9). This is most probably due to a change in reduced mass and bond strength; leading to reorder of vibration modes. The intensity of the Ir spectrum relates to the amplitude of oscillation. The higher the amplitude the higher larger the intensity.
And comparing the vibrating animation of both molecules, in BH3, Boron and hydrogen did vibrate relative to each other, while in the case of GaBr3 only Ga is moving. Usually, the stom with relatively lighter mass will vibrate will a larger amplitude than the one that is heavier.

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:29:17Z

Mhl12: /* Vibrational Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but in our frequency analysis, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:28:38Z

Mhl12: /* Structural Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

We can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" /> In simple, chemical bond is a 'link' between two atoms/groups, with attractive forces acting on both atoms/groups.

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:18:28Z

Mhl12: /* Structural Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In GaussView, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond. This always happens during the optimization process, when GaussView try to optimize the bond length.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:16:52Z

Mhl12: /* Structural Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion:

In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T10:14:21Z

Mhl12: /* Calculated MO and LCAO */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|800px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T03:24:48Z

Mhl12: /* References */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
1.<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
2.<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T03:24:28Z

Mhl12: /* References */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html
<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html

Rep:Mod:mhl12comp

2014-11-21T03:24:03Z

Mhl12: /* References */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html</ref>
</references>
<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html </ref>
</references>

Rep:Mod:mhl12comp

2014-11-21T03:23:39Z

Mhl12: /* References */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
<ref name="http://goldbook.iupac.org/CT07009.html" />http://goldbook.iupac.org/CT07009.html</ref>
<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html </ref>
</references>

Rep:Mod:mhl12comp

2014-11-21T03:22:40Z

Mhl12: /* NBO analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

==References==
<ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />http://science.jrank.org/pages/984/Bond-Energy.html </ref>
</references>

Rep:Mod:mhl12comp

2014-11-21T03:19:54Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
A molecule must have stretch or bent and created a change in dipole in order to be IR active. Hence, the higher the symmetry of molecules, the less IR active band exist due to many symmetric stretches and bent will not create a change in dipole.
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.
Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

Rep:Mod:mhl12comp

2014-11-21T03:16:27Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands. Bridging halide- Al stretch gives a lower wavenumber, it is most probably due to the reasoning that the bond length has become substantially longer than that of terminal halide-Al. The reasoning could be found on the discussion of vibrational frequency of Ga-Br and B-H.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

Rep:Mod:mhl12comp

2014-11-21T03:13:58Z

Mhl12: /* NBO analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

The bonding orbitals of Al, Cl and Br are sp3 hybridized.

Rep:Mod:mhl12comp

2014-11-21T03:11:13Z

Mhl12: /* NBO analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===
<pre>
(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.96691) BD ( 1)Al 1 -Cl 3
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 -0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 -0.0356
0.0000 0.0121 0.0191
2. (1.96691) BD ( 1)Al 1 -Cl 4
( 12.14%) 0.3484*Al 1 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 -0.0011 0.4501 0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 0.1524
0.0000 0.0816 0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 -0.0002 0.4859 0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 0.0356
0.0000 0.0121 0.0191
3. (1.96807) BD ( 1)Al 1 -Br 7
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 7 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 0.7662
0.0230 0.0000 0.0000
4. (1.96807) BD ( 1)Al 1 -Br 8
( 21.17%) 0.4601*Al 1 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 0.0001
0.4361 0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 8 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 -0.4319 -0.0109 -0.7662
-0.0230 0.0000 0.0000
5. (1.96691) BD ( 1)Al 2 -Cl 3
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
-0.0002 -0.6887 -0.0496 0.0000 -0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 3 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 0.5131 -0.0036 0.0000 -0.0356
0.0000 -0.0121 -0.0191
6. (1.96691) BD ( 1)Al 2 -Cl 4
( 12.14%) 0.3484*Al 2 s( 20.28%)p 3.77( 76.46%)d 0.16( 3.26%)
0.0000 0.0011 -0.4501 -0.0142 0.0003
-0.5362 -0.0191 0.0000 0.0000 0.0000
0.0002 0.6887 0.0496 0.0000 0.1524
0.0000 -0.0816 -0.0519
( 87.86%) 0.9374*Cl 4 s( 23.62%)p 3.23( 76.20%)d 0.01( 0.18%)
0.0000 0.0002 -0.4859 -0.0120 0.0000
0.7062 0.0012 0.0000 0.0000 0.0000
0.0000 -0.5131 0.0036 0.0000 0.0356
0.0000 -0.0121 -0.0191
7. (1.96807) BD ( 1)Al 2 -Br 5
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 0.6941 0.0568
0.0000 0.0000 0.0000 -0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 5 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 -0.7662
-0.0230 0.0000 0.0000
8. (1.96807) BD ( 1)Al 2 -Br 6
( 21.17%) 0.4601*Al 2 s( 29.66%)p 2.28( 67.62%)d 0.09( 2.73%)
0.0000 -0.0001 0.5445 -0.0056 -0.0001
-0.4361 -0.0324 0.0000 -0.6941 -0.0568
0.0000 0.0000 0.0000 0.1228 0.0000
0.0000 -0.0847 -0.0708
( 78.83%) 0.8878*Br 6 s( 22.57%)p 3.43( 77.43%)
0.4751 -0.0033 0.4319 0.0109 0.7662
0.0230 0.0000 0.0000
</pre>

Rep:Mod:mhl12comp

2014-11-21T02:59:16Z

Mhl12: /* 2nd Week Project - Lewis Acids and Bases */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

===NBO analysis===

File:Mhl12 bh3 mo.PNG

2014-11-21T02:57:18Z

Mhl12:

Rep:Mod:mhl12comp

2014-11-21T02:57:01Z

Mhl12: /* Calculated MO and LCAO */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_mo.PNG|500px]]

<pre>
LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)
</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

Rep:Mod:mhl12comp

2014-11-21T02:51:35Z

Mhl12: /* Calculated MO and LCAO */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

The calculated MO agrees with the LCAO approximation.

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

Rep:Mod:mhl12comp

2014-11-21T02:47:58Z

Mhl12: /* Bond orbital/ Coefficients/ Hybrids */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

BD refers to bonding orbital, CR refers to core orbital and LP refers to lone pair. The first, second and third BD shows that N-H orbital, which 69% contributed by nitrogen atoms. And nitrogen orbital is sp3 hybridized while H orbital is purely s.
The core orbital of nitrogen are purely s. The lone pair of nitrogen is sp3 hybridised as well.

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

Rep:Mod:mhl12comp

2014-11-21T02:42:01Z

Mhl12: /* Optimization of Al2Cl2Br4 */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging atom and aluminium has a longer bond length indicates that it is not a conventional 2c-2e bond.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

Rep:Mod:mhl12comp

2014-11-21T02:40:29Z

Mhl12: /* MO Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}
Strong bonding -> Medium bonding -> Weak bonding -> Medium antibonding -> Strong antibonding

File:Strong antibonding.JPG

2014-11-21T02:37:47Z

Mhl12:

File:Medium antibonding.JPG

2014-11-21T02:36:59Z

Mhl12:

File:Weak bonding.JPG

2014-11-21T02:36:40Z

Mhl12:

File:Medium bonding.JPG

2014-11-21T02:36:17Z

Mhl12:

File:Strong bonding.JPG

2014-11-21T02:35:52Z

Mhl12:

Rep:Mod:mhl12comp

2014-11-21T02:34:30Z

Mhl12: /* MO Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

{| border=1
|-
|[[File:strong bonding.JPG|300px]]
|[[File:medium bonding.JPG|300px]]
|[[File:weak bonding.JPG|300px]]
|[[File:medium antibonding.JPG|300px]]
|[[File:strong antibonding.JPG|300px]]
|-
|}

Rep:Mod:mhl12comp

2014-11-21T00:18:29Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Isomer has the lowest energy indicates that it is the most stable isomer. As we exchange one bridging Cl with one terminal Br, the energy increases by 13.58 kJ/mol, and increases another 13.06 kJ/mol to 26.14 kJ/mol as we remove one more bridging Cl. And the cis/trans configuration of Cl (isomer 3 and 4) does not have significant changes in energy. From the evidence above, it is likely that Cl is more favourable as bridging atom than Br. This is probably due to Cl, with higher electronegativities, are more compatible with the high lewis acidity Al atom.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:55:20Z

Mhl12: /* Optimization of Al2Cl2Br4 */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:53:38Z

Mhl12: /* Discussion */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Energy reported / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / a.u.'''
| align="center" style="background:#f0f0f0;"|'''Relative Energy / KJ/mol'''
|-
| align="center" style="background:#f0f0f0;"|Isomer 1 || -1458.35116016 || 0 || 0
|-
| align="center" style="background:#f0f0f0;"|Isomer 2 || -1458.34598708 || 0.00517308 || 13.58
|-
| align="center" style="background:#f0f0f0;"|Isomer 3 || -1458.34122428 || 0.00993588 || 26.14
|-
| align="center" style="background:#f0f0f0;"|Isomer 4 || -1458.34120346 || 0.00995670 || 26.14
|-
|}

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:45:21Z

Mhl12: /* Optimization of Al2Cl2Br4 */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:42:57Z

Mhl12: /* Discussion of position of the Br atoms */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:33:42Z

Mhl12: /* Population Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

Nitrogen is a more electronegative atoms and hence has a more negative dipole. And since NH3 is a neutral molecule, hence the dipole will adds up and give 0.

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:31:32Z

Mhl12: /* Vibrational Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect. It agrees with our calculation; GaBr3 IR spectrum has bands ranging from 70-300, while BH3 IR spectrum ranges from 1000-3000

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?

In this lab, all comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable. Frequency analysis is to make sure the optimisation process does provide a minima. Low frequencies in the calculation represents translational and rotational motion which should be excluded from the vibrational spectrum.

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:27:50Z

Mhl12: /* Frequency and Vibrational Analysis */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
now compare and contrast the vibrational spectra for BH3, and GaBr3. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect.

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?
answer ALL of the following questions in your wiki

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
All comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable.

What is the purpose of carrying out a frequency analysis?
Frequency analysis is to make sure. Low frequencies in the calculation represents translational motion which should be excluded from the vibrational spectrum.
What do the "Low frequencies" represent?

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T23:26:40Z

Mhl12: /* Vibrational Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency and Vibrational Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
now compare and contrast the vibrational spectra for BH3, and GaBr3. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are:
Anharmonic oscillator/ Morse curve, a better empirical curve fits the experimental better, but for the purpose of this lab, we assumed that the vibration works under harmonic oscillation;this means that if we stretch/compress the spring and release it, it will oscillate around its equilibrium position sinusoidally.

F=-ks(r-r0), where ks is the spring constant, r is the length of extension/compression, r0 is the equilibrium length.

ω=(ks/μ)0.5, where μ=reduced mass

ευ=[(υ+1/2)ω]/(2πc) where υ= 0,1,2,3,......

Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, or in this case we can treat bond strength as 'spring constant', and hence reduces the vibrational frequency. Of course, the reduced mass of both systems does affect the vibrational frequency as well. The higher the reduced mass, Ga-Br(36.8) compare to B-H(0.9), the lower the frequency of wave number. This is rationalized using Hooke's law without considering any relativistic effect or isotopes effect.

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?
answer ALL of the following questions in your wiki

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
All comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable.

What is the purpose of carrying out a frequency analysis?
Frequency analysis is to make sure. Low frequencies in the calculation represents translational motion which should be excluded from the vibrational spectrum.
What do the "Low frequencies" represent?

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T22:56:41Z

Mhl12: /* Structural Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency and Vibrational Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

For dative bond:
Dative bond is a slightly special case. It is a covalent bond but with a significant dipole on the chemical bond. The more electronegative atom will carry partial negative charge and the more electropositive atom will carry partial positive charge.

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
now compare and contrast the vibrational spectra for BH3, and GaBr3. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are:
Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, and hence reduces the vibrational frequency. This is rationalized using Hooke's law without considering any relativistic effect.

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?
answer ALL of the following questions in your wiki

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
All comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable.

What is the purpose of carrying out a frequency analysis?
Frequency analysis is to make sure. Low frequencies in the calculation represents translational motion which should be excluded from the vibrational spectrum.
What do the "Low frequencies" represent?

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]

Rep:Mod:mhl12comp

2014-11-20T22:50:30Z

Mhl12: /* Structural Comparison */

==Comparison of BH3, BBr3 and GaBr3==
===BH3===
====B3LYP/3-21G level====

Optimisation log file [[Media:MHL12 BH3 OPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_BH3_OPT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_BH3_REOPT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_bh3_reopt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000867 0.001800 YES
RMS Displacement 0.000415 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.19
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency and Vibrational Analysis=====

Frequency file: [[Media:MHL12_BH3_REOPT_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_bh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -10.1940 -10.1821 -3.1776 -0.0012 0.0579 0.4920
Low frequencies --- 1162.9850 1213.1461 1213.1463
</pre>

|}

======Vibrational spectrum for BH3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1163
|93
|yes
|bend
|-
|1213
|14
|no
|bend
|-
|1213
|14
|very slight
|bend
|-
|2583
|0
|no
|stretch
|-
|2716
|126
|yes
|stretch
|-
|2716
|126
|yes
|stretch
|-
|}

[[File:mhl12_bh3_reopt_freq_spectrum.PNG|300px]]

=====Calculated MO and LCAO=====

MO checkpoint file: [[Media:MHL12_BH3_OPT_631G-MO.chk|file]]

[[File:mhl12_bh3_MO_diagram_1-8.PNG|500px]]

[[File:mhl12_bh3_lcao.PNG|300px]]

<pre>

top diagram: Calculated MO
Bottom Diagram: LCAO MO (Credit to Dr Tricia Hunt, diagram adapted from Year 2 Lecture 4 Tutorial Problem Model Answers)

</pre>

===BBr3===

====B3LYP/6-31(d,p)LANL2DZ====

Optimisation log file [[Media:mhl12_bbr3_opt.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:mhl12_bbr3_opt_summary.PNG|300px]]
|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000023 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_bh3_opt_631g_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 1.93
|-
| θ(X-E-X) degrees(º) || 120.0
|}

===GaBr3===

====B3LYP/LanL2DZ====

{{DOI|10042/84995}}

Optimisation log file [[Media:mhl12_gabr3_opt_log.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_gabr3_opt_summary.PNG|300px]]

|<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000003 0.001800 YES
RMS Displacement 0.000002 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_gabr3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

=====Geometry Data=====

{| class="wikitable"
|-
| r(E-X) Å || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0
|}

=====Frequency Analysis=====

Frequency file: [[Media:MHL12_GABR3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_gabr3_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.5293 -0.5288 -0.0024 -0.0010 0.0233 1.1993
Low frequencies --- 76.3744 76.3753 99.6981
</pre>

|}

======Vibrational spectrum for GaBr3======
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|76
|3
|no
|bend
|-
|76
|3
|no
|bend
|-
|100
|9
|very slight
|bend
|-
|197
|0
|no
|stretch
|-
|316
|57
|yes
|stretch
|-
|316
|57
|yes
|stretch
|-
|}

[[File:mhl12_gabr3_freq_spectrum.PNG|300px]]

===Structural Comparison===

Geometry Data

{| class="wikitable"
! !! BH3 !! BBr3 !! GaBr3
|-
| r(E-X) Å || 1.19 || 1.93 || 2.35
|-
| θ(X-E-X) degrees(º) || 120.0 || 120.0 || 120.0
|}

Discussion
In gaussview, when it thinks the bond length is too long (than its threshold) or the bonding energy is unfavorable, it will not show the bond.

we can see that the bond length increases from B-H (BH3) to B-Br (BBr3) This is mostly due to the increase in radii of ligands; the mismatch in orbital size causes weaker interaction and thus a larger bond length.
Boron and Gallium both belong to Group 13. Here again, down the group radii of Ga is larger than that of B. Hence the bond length of Ga-Br is larger than that of B-Br. However comparing the increment of B-H to B-Br (0.74Å) and B-Br to Ga-Br(0.42Å), the effect of changing a different nature or substantially larger ligand lead to a larger change in bond distance. Chaging the centre atom will lead to corresponding change according to their ionic radii.

Definition of chemical bond (from [[http://goldbook.iupac.org/CT07009.html]]) : When forces acting between two atoms or groups of atoms lead to the formation of a stable independent molecular entity, a chemical bond is considered to exist between these atoms or groups. The principal characteristic of a bond in a molecule is the existence of a region between the nuclei of constant potential contours that allows the potential energy to improve substantially by atomic contraction at the expense of only a small increase in kinetic energy. Not only directed covalent bonds characteristic of organic compounds, but also bonds such as those existing between sodium cations and chloride anions in a crystal of sodium chloride or the bonds binding aluminium to six molecules of water in its environment, and even weak bonds that link two molecules of O2 into O4, are to be attributed to chemical bonds. <ref name="http://goldbook.iupac.org/CT07009.html" />

For covalent bond:
Taking silica, a stable and abundant compound on Earth, as a benchmark, Si-O having a bond energy of 452 kJ/mol; so bonding energy above 450 kJ/mol, such as multiple bonding C≡N, N≡N, C=O etc., could be considered as very strong bond; however for single bonding, Si-O is one of the strongest bond.
Typical C-C bond has a value of 346 kJ/mol which is around 20% lower in energy than that of Si-O. C-C still could be considered a strong bond.
Bonding energies which is 50% less than Si-O (say 200 kJ/mol) are considered medium bond. N-N, N-B etc. have bonding energies of 100+ kJ/mol.
Bonding energies which is below 100 kJ/mol (an order of magnitude lower than majority of covalent bonding energy)

For ionic bond:
Ionic bonds generally have higher bonding energy, ranging from 700-4000 <ref name="http://science.jrank.org/pages/984/Bond-Energy.html" />

However, usually molecules have the characteristics of both ionic bond and covalent bond in itself. Hence theoretical calculation of bond energy does not always agree with the observed bond energy.

===Vibrational Comparison===

Refer to [[#Frequency_Analysis|BH3]] and [[#Frequency_Analysis_2|GaBr3]]

Discussion:
now compare and contrast the vibrational spectra for BH3, and GaBr3. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are:
Bond length of B-H is considerably shorter than that of Ga-Br. Generally, increment in bond length reduces the bond strength, and hence reduces the vibrational frequency. This is rationalized using Hooke's law without considering any relativistic effect.

There been a reordering of modes! This can be seen particularly in relation to the A2" umbrella motion. Compare the relative frequency and intensity of the umbrella motion for the two molecules. Looking at the displacement vectors how has the nature of the vibration changed? Why?
answer ALL of the following questions in your wiki

Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
All comparison should be run under same basis set. This is to compare two things in a same manner; basis could be thought as a fixed variable, and an experiment should only have one responding variable.

What is the purpose of carrying out a frequency analysis?
Frequency analysis is to make sure. Low frequencies in the calculation represents translational motion which should be excluded from the vibrational spectrum.
What do the "Low frequencies" represent?

==Bonding analysis of NH3BH3==

===BH3===

B3LYP/6-31G(d,p) level optimisation and frequency analysis, refer to [[#B3LYP.2F6-31G.28d.2Cp.29_level|here]]

===NH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3_REOPT-631.LOG| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3_reopt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000012 0.001800 YES
RMS Displacement 0.000008 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3_OPT-631.JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Geometry Data====

====Frequency====

{{DOI|10042/90430}}

Frequency file: [[Media:MHL12_NH3_FREQ.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3_reopt_freq_summary.PNG|300px]]

|

<pre>
Low frequencies --- -0.0129 -0.0027 0.0005 7.0724 8.1020 8.1023
Low frequencies --- 1089.3849 1693.9369 1693.9369
</pre>

|}

=====Vibrational spectrum for NH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1089
|145
|yes
|bend
|-
|1694
|14
|very slight
|bend
|-
|1694
|14
|very slight
|bend
|-
|3461
|1
|no
|stretch
|-
|3590
|0
|no
|stretch
|-
|3590
|0
|no
|stretch
|}

[[File:mhl12_nh3_spectrum.PNG|300px]]

====Population Analysis====

NBO analysis log:[[Media:MHL12_NH3_MO.txt| here]]

[[File:mhl12_nh3_nbo-analysis.PNG|300px]]

=====Bond orbital/ Coefficients/ Hybrids=====

<pre>

(Occupancy) Bond orbital/ Coefficients/ Hybrids
---------------------------------------------------------------------------------
1. (1.99909) BD ( 1) N 1 - H 2
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.0000
0.0000 0.8155 0.0277 -0.2910 0.0052
0.0000 0.0000 -0.0281 -0.0087 0.0013
( 31.17%) 0.5583* H 2 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0000 -0.0289 0.0072
2. (1.99909) BD ( 1) N 1 - H 3
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 -0.7062
-0.0239 -0.4077 -0.0138 -0.2910 0.0052
0.0076 0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 3 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 0.0250 0.0145 0.0072
3. (1.99909) BD ( 1) N 1 - H 4
( 68.83%) 0.8297* N 1 s( 24.86%)p 3.02( 75.05%)d 0.00( 0.09%)
0.0001 0.4986 0.0059 0.0000 0.7062
0.0239 -0.4077 -0.0138 -0.2910 0.0052
-0.0076 -0.0243 0.0140 0.0044 0.0013
( 31.17%) 0.5583* H 4 s( 99.91%)p 0.00( 0.09%)
0.9996 0.0000 -0.0250 0.0145 0.0072
4. (1.99982) CR ( 1) N 1 s(100.00%)
1.0000 -0.0002 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
0.0000 0.0000 0.0000 0.0000 0.0000
5. (1.99721) LP ( 1) N 1 s( 25.38%)p 2.94( 74.52%)d 0.00( 0.10%)
0.0001 0.5036 -0.0120 0.0000 0.0000
0.0000 0.0000 0.0000 0.8618 -0.0505
0.0000 0.0000 0.0000 0.0000 -0.0310
6. (0.00000) RY*( 1) N 1 s( 99.98%)p 0.00( 0.02%)d 0.00( 0.00%)

</pre>

===NH3BH3===

====B3LYP/6-31G(d,p) level====

Optimisation log file [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT.txt| here]]
{| class="wikitable"
|+
! summary data !! convergence || Jmol

|-

|[[File:mhl12_nh3bh3_opt_summary.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000022 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised GaBr3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>MHL12_NH3BH3_631-DP_REOPT-TIGHT_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency analysis====

Frequency file: [[Media:MHL12_NH3BH3_631-DP_REOPT-TIGHT_FREQ_C3V.txt| here]]

{| class="wikitable"
|+
! summary data || low modes

|-

|[[File:mhl12_nh3bh3_reopt_summary.PNG|300px]]

|

<pre>
Low frequencies --- -5.8792 -0.3571 -0.0537 -0.0014 1.0077 1.1094
Low frequencies --- 263.2802 632.9504 638.4510
</pre>

|}

=====Vibrational spectrum for NH3BH3=====
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|262
|0
|no
|bend
|-
|633
|14
|very slight
|stretch
|-
|638
|4
|no
|bend
|-
|638
|4
|no
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|109
|yes
|bend
|-
|1204
|3
|no
|bend
|-
|1204
|3
|no
|bend
|-
|1676
|28
|yes
|bend
|-
|1676
|28
|yes
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|no
|stretch
|-
|3581
|28
|yes
|stretch
|-
|3581
|28
|yes
|stretch
|-
|}

[[File:mhl12_nh3bh3_spectrum.PNG|300px]]

====Bond Energy====

E(NH3)= -56.55776873 a.u.

E(BH3)= -26.61532364 a.u.

E(NH3BH3)= -83.22468908 a.u.

ΔE=E(NH3BH3) - [E(NH3)+E(BH3)]

= -83.22468908 a.u. - [-56.55776873 a.u. -26.61532364 a.u.]

= -0.05159671 a.u.

= -135.47 kJ/mol (2 d.p.)

Discussion: C-C bond which is isoelectronic to N-B bond; typical C-C bond has a bond energy of 346kJ/mol. Hence N-B bond is slightly weaker bond relative to C-C bond. Considering that bond energy of N-B is still of the same order of magnitude with C-C bond, and the fact that the bond energy is way above interaction of hydrogen bonding (typical value 8-30 kJ/mol, except F-H-F), it can be said that N-B bond is a medium(strength) bonding.

==2nd Week Project - Lewis Acids and Bases==

===Optimization of Al2Cl2Br4===

The optimization process was computed using 'GEN' basis set and keywords ''pseudo=cards gfinput''. This allow us to specify basis set for each atoms individually.
The following instructions were added into the gjf files:
<pre>

Al 0
6-31G(d,p)
****
Cl 0
6-31G(d,p)
****
Br 0
LanL2DZ
****

Br 0
LanL2DZ

</pre>

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|
|<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso1_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso2_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso3_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
||
<jmol><jmolApplet>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>mhl12_iso4_opt_JMOL.mol</uploadedFileContents>
</jmolApplet></jmol>
|-
| align="center" style="background:#f0f0f0;"|Covergence Data
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000008 0.000060 YES
RMS Displacement 0.000003 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000017 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000018 0.000060 YES
RMS Displacement 0.000007 0.000040 YES

</pre>
||
<pre>
Item Value Threshold Converged?
Maximum Force 0.000001 0.000015 YES
RMS Force 0.000000 0.000010 YES
Maximum Displacement 0.000016 0.000060 YES
RMS Displacement 0.000005 0.000040 YES

</pre>
|-
| align="center" style="background:#f0f0f0;"|File Type||.log||.log||.log ||.log
|-
| align="center" style="background:#f0f0f0;"|Calculation Type||FOPT||FOPT||FOPT||FOPT
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen||Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122428||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.00000222||0.00000255||0.00000034||0.00000034
|-
| align="center" style="background:#f0f0f0;"|Imaginary Freq||||||||
|-
| align="center" style="background:#f0f0f0;"|Dipole Moment / Debye||0.0002||0.1240||0.0002||0.1707
|-
| align="center" style="background:#f0f0f0;"|Point Group||C1||C1||C1||C1
|-
| align="center" style="background:#f0f0f0;"|Job cpu time||0 days 0 hours 5 minutes 38.8 seconds||0 days 0 hours 17 minutes 56.6 seconds|| 0 days 0 hours 10 minutes 9.1 seconds|||0 days 0 hours 12 minutes 48.1 seconds
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107512}}||{{DOI|10042/107510}}||{{DOI|10042/107508}}||{{DOI|10042/107506}}
|}

All calculations have been confirmed with the convergence of the data. The optimization will then be further confirmed with frequency analysis (±15cm-1 for the low frequencies mode as a benchmark to check the optimization process)

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;" width="50"|'''''
| align="center" style="background:#f0f0f0;"|'''Computational bond length / Å'''
| align="center" style="background:#f0f0f0;"|'''Literature bond length / Å'''
|-
| align="center" style="background:#f0f0f0;"|Terminal Br-Al || 2.28
|-
| align="center" style="background:#f0f0f0;"|Terminal Cl-Al || 2.09
|-
| align="center" style="background:#f0f0f0;"|Bridging Br-Al || 2.49
|-
| align="center" style="background:#f0f0f0;"|Bridging Cl-Al || 2.30
|-
|}

To determine the reliability of the C-O bond lengths these can be compared to the value for free C=O which is 1.21Α<ref name=refcrc5></ref>. The value found for the Fe complex has an absolute difference of 0.06Α and the values for CO are all within reason when compared to the literature value.

====Discussion of position of the Br atoms====

Bridging bromine is slightly unfavorable as shown by the energy above.

====Dissociation energy====

E(Al2Cl2Br4)= -1458.35116016 a.u.

E(AlClBr2)= -26.61532364 a.u. *Refer to {{DOI|10042/107530}}

ΔE=E(Al2Cl2Br4) - 2*E(AlClBr2)

= -1458.35116016 a.u. - 2*[ -729.15823878 a.u.]

= -0.0346826 a.u.

= -91.06 kJ/mol (2 d.p.)

===Frequency Analysis===

{| class="wikitable" border="1" {{table}}
| align="center" style="background:#f0f0f0;"|Compound
| '''Isomer 1'''
| '''Isomer 2'''
| '''Isomer 3'''
| '''Isomer 4'''
|-
| align="center" style="background:#f0f0f0;"|Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| align="center" style="background:#f0f0f0;"|Basis Set||Gen||Gen||Gen|Gen
|-
| align="center" style="background:#f0f0f0;"|Charge||0||0||0||0
|-
| align="center" style="background:#f0f0f0;"|Spin||Singlet||Singlet||Singlet||Singlet
|-
| align="center" style="background:#f0f0f0;"|E(RB3LYP) / a.u.||-1458.35116016||-1458.34598708||-1458.34122763||-1458.34120346
|-
| align="center" style="background:#f0f0f0;"|RMS Gradient Norm / a.u.||0.0000441||0.00000255||0.00000753||0.00000064
|-
|align="center" style="background:#f0f0f0;" |Imaginary Freq||0||0||0||0
|-
|align="center" style="background:#f0f0f0;" |Dipole Moment / Debye||0.0000 ||0.1240 ||0.0000 ||0.1707
|-
|align="center" style="background:yellow;" |Point Group||style="background:yellow;" |D2H ||style="background:yellow;" | C1||style="background:yellow;" |C2H ||style="background:yellow;" |C2V
|-
|align="center" style="background:#f0f0f0;"|Job cpu time|| || 0 days 0 hours 2 minutes 22.4seconds||0 days 0 hours 1 minutes 0.9seconds ||
|-
|align="center" style="background:#f0f0f0;" |Low Modes
||
<pre>
Low frequencies --- -3.5251 -2.2048 -0.0030 -0.0022 -0.0019 1.9779
Low frequencies --- 15.0148 38.6160 59.6441
</pre>

||
<pre>
Low frequencies --- -2.6621 -0.0021 -0.0018 0.0018 2.1611 3.3401
Low frequencies --- 14.5344 44.1267 64.0506
</pre>

||
<pre>
Low frequencies --- -5.0200 -3.3842 -3.0570 0.0035 0.0039 0.0041
Low frequencies --- 12.4814 47.7011 67.3961
</pre>

||
<pre>
Low frequencies --- -4.8432 -3.3720 -3.0141 -0.0025 -0.0016 0.0013
Low frequencies --- 12.2710 49.9139 71.1649
</pre>
|-
| align="center" style="background:#f0f0f0;"|D-Space Link||{{DOI|10042/107492}}||{{DOI|10042/107490}}||{{DOI|10042/107488}}||{{DOI|10042/107486}}
|-
| align="center" style="background:#f0f0f0;"|IR Spectra
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend (scissors)
|-
|39
|0
|No
|Bend (twisting)
|-
|60
|0
|No
|Bend (scissors)
|-
|83
|0
|No
|Bend (Twisting)
|-
|97
|8
|Yes
|Bend
|-
|101
|7
|Yes
|Bend
|-
|105
|0
|No
|Bend
|-
|145
|0
|No
|Bend
|-
|158
|5
|Yes
|Bend
|-
|158
|0
|No
|Bend
|-
|243
|6
|Yes
|Bend
|-
|261
|0
|No
|Asymmetric Cl Al stretch
|-
|291
|0
|No
|Symmetric Terminal Br Al stretch
|-
|400
|463
|Yes
|Symmetric Terminal Br Al stretch
|-
|408
|139
|Yes
|Bend
|-
|445
|0
|No
|symmetric Bridging Cl Al stretch
|-
|491
|0
|No
|Antisymmetric Terminal Br Al stretch
|-
|501
|289
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|}
[[File:mhl12_iso1_freq_spectrum.PNG|400px]]
||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|15
|0
|No
|Bend
|-
|44
|0
|No
|Bend
|-
|64
|0
|No
|Bend
|-
|82
|1
|No
|Bend
|-
|88
|0
|No
|Bend
|-
|95
|4
|Slightly
|Bend
|-
|104
|6
|Yes
|Bend
|-
|135
|3
|Yes
|Bend
|-
|141
|5
|Yes
|Bend
|-
|163
|0
|No
|Bend
|-
|200
|17
|Yes
|Asymmetric Bridging Br Al stretch
|-
|238
|7
|Slightly
|Symmetric Terminal Br Al stretch
|-
|265
|13
|Yes
|Asymmetric Bridging Cl Al stretch
|-
|374
|149
|Yes
|Symmetric bridging Br stretch
|-
|395
|374
|Yes
|Terminal Br Al stretch
|-
|438
|32
|Yes
|Bridging Br bend
|-
|496
|132
|Yes
|Antisymmetric Terminal Br Al stretch
|-
|575
|170
|Yes
|Terminal Al Cl stretch
|}
[[File:mhl12_iso2_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|48
|0
|No
|Bend
|-
|67
|0
|No
|Bend
|-
|76
|0
|No
|Bend
|-
|98
|4
|Yes
|Bend
|-
|98
|0
|No
|Bend
|-
|105
|5
|Yes
|Bend
|-
|123
|7
|Yes
|Bend
|-
|125
|0
|No
|Bend
|-
|151
|0
|No
|Bend
|-
|193
|0
|No
|Bend
|-
|216
|58
|Yes
|Bend
|-
|218
|0
|No
|Symmetric ring breathing
|-
|334
|147
|Yes
|Bridging Br Al stretch
|-
|398
|374
|Yes
|Asymmetric Terminal Br Al stretch
|-
|426
|0
|No
|Terminal Br Al stretch
|-
|571
|0
|No
|Symmetric Terminal Cl Al stretch
|-
|576
|314
|Yes
|Asymmetric Terminal Cl Al stretch
|-
|}
[[File:mhl12_iso3_freq_spectrum.PNG|400px]]

||
{| border=1
|-
! Wavenumber
! Intensity
! IR active?
! Mode
|-
|12
|0
|No
|Bend
|-
|50
|0
|No
|Bend
|-
|71
|0
|No
|Bend
|-
|73
|0
|
|
|-
|90
|0
|
|
|-
|99
|3
|YES/NO
|Bend
|-
|111
|7
|Yes
|Bend
|-
|123
|5
|Yes
|Bend
|-
|124
|0
|No
|Bend
|-
|152
|0
|No
|Bend
|-
|193
|0
|No
|Antisymmetric Bridging Br Al stretch
|-
|216
|57
|Yes
|Symmetric Bridging Br Al stretch
|-
|219
|1
|No
|Symmetric Bridging Br Al stretch
|-
|334
|147
|Yes
|Symmetric Bridging Br Al stretch
|-
|397
|348
|Yes
|Terminal Br/Cl Al stretch
|-
|427
|29
|Yes
|Terminal Br/Cl Al stretch
|-
|569
|31
|Yes
|Terminal Br/Cl Al stretch
|-
|578
|282
|Yes
|Terminal Br/Cl Al stretch
|-
|}
[[File:mhl12_iso4_freq_spectrum.PNG|400px]]
|}
====Discussion====
The point groups of the four isomers above are highlighted in the table. Isomer 2 belongs to C1 group, the group with only E symmetry elements, thus it has the most IR bands. The other 3 isomers have higher symmetry, hence they have less IR bands.

===MO Analysis===

5 MOs of Isomer 1 of Al2Cl2Br4 are investigated for this project. All files for MO analysis can be obtained from {{DOI|10042/107495}}

[[File:mhl12_iso1_mo_1.jpg]]