ChemWiki - User contributions [en]

User:Yz13712

2015-02-13T13:54:31Z

Yz13712: /* Validity of the traditional [N(R4]+ description */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast:

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions:

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R)4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of [N(CH3)3(CH2OH)]+===

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

User:Yz13712

2015-02-12T16:29:08Z

Yz13712: /* Optimization of [S(CH3)3]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast:

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions:

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of [N(CH3)3(CH2OH)]+===

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

User:Yz13712

2015-02-12T16:28:56Z

Yz13712: /* Optimization of [S(CH3)3]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast:

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions:

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Csv

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of [N(CH3)3(CH2OH)]+===

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

User:Yz13712

2015-02-12T16:21:11Z

Yz13712: /* Vibrational spectrum for GaBr3 */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast:

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions:

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of [N(CH3)3(CH2OH)]+===

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

User:Yz13712

2015-02-12T16:18:12Z

Yz13712: /* Interesting aspect of the structure of [N(CH3)3(CH2OH)]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of [N(CH3)3(CH2OH)]+===

During the optimization of [N(CH3)3(CH2OH)]+, there are two possible structure (Symmetry) for which O-H bond could be both periplanar or antiperiplanar to the next C-N bond. The result shows that periplanar structure are preferred since the two lone pair electrons in O atom is favoring on opposite site with two adjacent C-H bond. These could be explained by both steric effect and stabilization of C-H anti-bonding orbital.

User:Yz13712

2015-02-12T16:09:22Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934 (degenerate)
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

The HOMO of [N(CH3)4]+ molecule is triply degenerate due to the Td symmetry. When one methyl group was replaced by -OH or -CN group, this degeneracy was broken and the structure became more stable due to the electronegative of O and N atom. The HOMO-LUMO gap also decreased.

===Interesting aspect of the structure of [N(CH3)3(CH2OH)]+===
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T16:03:37Z

Yz13712: /* Interesting aspect of the structure of [N(CH3)3(CH2OH)]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

===Interesting aspect of the structure of [N(CH3)3(CH2OH)]+===
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T16:00:22Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || -0.48763 || -0.50047 || -0.57934
|-
| LUMO || -0.12459 || -0.18183 || -0.13303
|-
| HOMO-LUMO gap (KJ•mol-1) || 953 || 837 || 1172
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

File:ROH lumo.PNG

2015-02-12T15:59:02Z

Yz13712: Yz13712 uploaded a new version of "File:ROH lumo.PNG"

File:ROH homo.PNG

2015-02-12T15:58:51Z

Yz13712: Yz13712 uploaded a new version of "File:ROH homo.PNG"

File:RCN lumo.PNG

2015-02-12T15:58:40Z

Yz13712: Yz13712 uploaded a new version of "File:RCN lumo.PNG"

File:RCN homo.PNG

2015-02-12T15:58:22Z

Yz13712: Yz13712 uploaded a new version of "File:RCN homo.PNG"

File:N LUMO.PNG

2015-02-12T15:58:11Z

Yz13712: Yz13712 uploaded a new version of "File:N LUMO.PNG"

File:N H)OMO.PNG

2015-02-12T15:58:00Z

Yz13712: Yz13712 uploaded a new version of "File:N H)OMO.PNG"

User:Yz13712

2015-02-12T15:49:33Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG]] || [[File:N H)OMO.PNG]]
|-
| LUMO || [[File:ROH lumo.PNG]] || [[File:RCN lumo.PNG]] || [[File:N LUMO.PNG]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:49:00Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG]] || [[File:RCN homo.PNG|300px]] || [[File:N H)OMO.PNG|300px]]
|-
| LUMO || [[File:ROH lumo.PNG|300px]] || [[File:RCN lumo.PNG|300px]] || [[File:N LUMO.PNG|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:48:06Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG|300px]] || [[File:RCN homo.PNG|300px]] || [[File:N H)OMO.PNG|300px]]
|-
| LUMO || [[File:ROH lumo.PNG|300px]] || [[File:RCN lumo.PNG|300px]] || [[File:N LUMO.PNG|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:47:22Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| HOMO || [[File:ROH homo.PNG|500px]] || [[File:RCN homo.PNG|500px]] || [[File:N H)OMO.PNG|500px]]
|-
| LUMO || [[File:ROH lumo.PNG|500px]] || [[File:RCN lumo.PNG|500px]] || [[File:N LUMO.PNG|500px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

File:RCN lumo.PNG

2015-02-12T15:46:59Z

Yz13712:

File:RCN homo.PNG

2015-02-12T15:46:37Z

Yz13712:

File:ROH lumo.PNG

2015-02-12T15:46:09Z

Yz13712:

File:ROH homo.PNG

2015-02-12T15:45:45Z

Yz13712:

File:N LUMO.PNG

2015-02-12T15:45:20Z

Yz13712:

File:N H)OMO.PNG

2015-02-12T15:43:47Z

Yz13712:

User:Yz13712

2015-02-12T15:32:13Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

Compare to the charge distribution of [N(CH3)4]+ molecule, OH group is an electron donating group and push the electrons towards the central atom which results in the increase charge value of Central N atom and other C and H atoms in the system. On the contrary, CN group is an electron withdrawing group which pull electrons from the central atom and results in the decrease value of N central atom.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:24:34Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+ !! [N(CH3)4]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN) || -0.295 (central atom)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN) || -0.483 (CH3)
|-
| charge on O || -0.757 || N/A || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309 || 0.269
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:21:10Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.313(central atom) || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN)
|-
| charge on O || -0.757 || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:20:30Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.313(CN) || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.489(CH3),-0.385 (the CH2 next to CN), 0.209((CN)
|-
| charge on O || -0.757 || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:19:32Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.313(CN) || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.385 (the CH2 next to CN), -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.757 || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:19:08Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.313(CN) || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.488, -0.489(CH3), 0.094(CH2OH) || -0.385 (the CH2 next to CN), -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.757 || N/A
|-
| charge on H || 0.264 to 0.285(CH3), 0.234(CH2OH), 0.532(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:11:45Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.322(CN) || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 (the CH2 next to CN), -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.725 || N/A
|-
| charge on H || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:09:45Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.322 || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 (the CH2 next to CN) -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.725 || N/A
|-
| charge on H || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || From 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:08:10Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !![N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.322 || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 to -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.725 || N/A
|-
| charge on H || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:07:38Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.322 || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 to -0.489(CH3), 0.209((CN)
|-
| charge on O || -0.725 || N/A
|-
| charge on H || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:07:10Z

Yz13712: /* Charge distribution comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.322 || -0.289(central atom), -0.186(CN)
|-
| charge on C || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 to -0.489(CH3), 0.209((CN)
|-
| charge on O || /A || -0.725 || N/A
|-
| charge on H || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 to 0.309
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:02:54Z

Yz13712: /* Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:01:53Z

Yz13712: /* HOMO and LUMO comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

User:Yz13712

2015-02-12T15:01:11Z

Yz13712: /* Interesting aspect of the structure of [N(CH3)3(CH2OH)]+ */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T14:47:05Z

Yz13712: /* Validity of the traditional [N(R4]+ description */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

The "formal" positive charge on the N in the traditional picture represents that the positive charge is on central N atom since N atom has "donated" one electron to an Lewis base to maintain its stable 8-electron structure and SP3 Hybridization.

However, if we look at the electronegativity of each atoms inside the molecule, we will see that the positive charge is well separated among the whole structure instead of fix at any atom position.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T14:31:29Z

Yz13712: /* [X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The C-X Bond interaction between all three molecules are roughly SP3 hybridization. This explain why Hyridization of X central orbitals are around 25% s + 75% p. P and S orbital contains a little d orbital contribution is because they are in the third row of Periodic Table. The hybridization of C atoms are also SP3 hybridization. Since C atom is connect to 3 H atoms and 1 X atom, the contribution of C orbital will be not exact to 25% s + 75% p.

The contribution from C to X is also strongly related to the electronegativities of X atoms. X atom with highest electronegativity (N atom) will also has the highest contribution since it attract electrons strongly.

===Validity of the traditional [N(R4]+ description===

''What does the "formal" positive charge on the N represent in the traditional picture?On what atoms is the positive charge actually located for this cation?''

The concept of formal charge is based on the traditional Lewis structure, in which electron pair is considered to be equally shared between any two bonding atoms regardless of their electronegativities. The definition of formal charge is therefore, the difference between the positive nuclear charge and the total number of electrons of an atom in a given molecule. <ref name="formalcharge" />

Based on this definition, the N atom in [N(R4]+ has a nuclear charge of 7 and total number of electrons of 6, of which 2 belong to the non-bonding inner shell (1s) and 4 are shared with the atoms in the R groups. Therefore, it has a formal charge of +1.

However, because the concept of Lewis structure does not take electronegativities into account, the assignment of +1 charge to the N atom in the case of [N(CH3)4]+ is not correct. The +1 positive charge is actually spread out over all of the H atoms in this cation.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T14:18:15Z

Yz13712: /* [X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

The orbitals form C, N, P, S that contribute to the C-X bonds are all roughly sp3 hybridised. However, the orbitals of P and S have a tiny bit of d orbital character because they are third row atoms, which means that 3d orbital is available to them.

From the table above, it can be seen as a general trend that the more electronegative atom between the C and X pair contributes more to the C-X bond. For example, N is more electronegative than C (3.04 vs. 2.55), and hence N contributes more to the C-N bond than C( 66% vs. 34%). This is because the more electronegative atom can attract more electron density than the less electronegative one, i.e. the electron density is more polarised towards the more electronegative atom, and therefore the more electronegative atom contributes more to the C-X bond. From a MO theory's point of view, the orbital that is used to construct the C-X bond of the more electronegative atom is lower in energy than the less electronegative one, which leads to the resulting bonding MO being closer in energy and similar in shape to the orbital of the more electronegative atom. Hence, we get the same conclusion that the more electronegative atom contributes more to the C-X bond.

===Validity of the traditional [N(R4]+ description===

''What does the "formal" positive charge on the N represent in the traditional picture?On what atoms is the positive charge actually located for this cation?''

The concept of formal charge is based on the traditional Lewis structure, in which electron pair is considered to be equally shared between any two bonding atoms regardless of their electronegativities. The definition of formal charge is therefore, the difference between the positive nuclear charge and the total number of electrons of an atom in a given molecule. <ref name="formalcharge" />

Based on this definition, the N atom in [N(R4]+ has a nuclear charge of 7 and total number of electrons of 6, of which 2 belong to the non-bonding inner shell (1s) and 4 are shared with the atoms in the R groups. Therefore, it has a formal charge of +1.

However, because the concept of Lewis structure does not take electronegativities into account, the assignment of +1 charge to the N atom in the case of [N(CH3)4]+ is not correct. The +1 positive charge is actually spread out over all of the H atoms in this cation.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T14:17:29Z

Yz13712: /* [X(CH3)y]+ Charge Distribution (NBO) Comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

''compare and contrast the relative contribution of the C and heteroatom to the C-X bond. How do your results relate to the charge distribution just studied?''

The orbitals form C, N, P, S that contribute to the C-X bonds are all roughly sp3 hybridised. However, the orbitals of P and S have a tiny bit of d orbital character because they are third row atoms, which means that 3d orbital is available to them.

From the table above, it can be seen as a general trend that the more electronegative atom between the C and X pair contributes more to the C-X bond. For example, N is more electronegative than C (3.04 vs. 2.55), and hence N contributes more to the C-N bond than C( 66% vs. 34%). This is because the more electronegative atom can attract more electron density than the less electronegative one, i.e. the electron density is more polarised towards the more electronegative atom, and therefore the more electronegative atom contributes more to the C-X bond. From a MO theory's point of view, the orbital that is used to construct the C-X bond of the more electronegative atom is lower in energy than the less electronegative one, which leads to the resulting bonding MO being closer in energy and similar in shape to the orbital of the more electronegative atom. Hence, we get the same conclusion that the more electronegative atom contributes more to the C-X bond.

===Validity of the traditional [N(R4]+ description===

''What does the "formal" positive charge on the N represent in the traditional picture?On what atoms is the positive charge actually located for this cation?''

The concept of formal charge is based on the traditional Lewis structure, in which electron pair is considered to be equally shared between any two bonding atoms regardless of their electronegativities. The definition of formal charge is therefore, the difference between the positive nuclear charge and the total number of electrons of an atom in a given molecule. <ref name="formalcharge" />

Based on this definition, the N atom in [N(R4]+ has a nuclear charge of 7 and total number of electrons of 6, of which 2 belong to the non-bonding inner shell (1s) and 4 are shared with the atoms in the R groups. Therefore, it has a formal charge of +1.

However, because the concept of Lewis structure does not take electronegativities into account, the assignment of +1 charge to the N atom in the case of [N(CH3)4]+ is not correct. The +1 positive charge is actually spread out over all of the H atoms in this cation.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T14:17:08Z

Yz13712: /* [X(CH3)y]+ Charge Distribution (NBO) Comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

The charge on N atom is negative value whereas charges on S and P is positive values and P atom has higher value. This is due to the electronegativity among this three atoms: N has the highest electronegativity value which means that N atom is the most powerful to attract electrons therefore has negative charge value. P atom, on the contrary, has lowest electronegativity value and gets highest positive charge value.

The values of charge on C atoms is closely related to the electronegativity of their neighboring central atoms. The higher the electronegativity of their neighboring central atom is, the lower charge value on C atom will get. Therefore, Carbon next to N atom has lowest negative charge value and Carbon next to P atom has highest negative charge value. The reason why the charge on C among all three molecules are negative is because they are all methyl group and Hydrogens next to C is very electropositive.

The charges on H nearly remains the same reflect that the central atom is too far away that could not have significant affect to Hydrogen atoms. The reason why there are two different Hydrogen environments on [S(CH3)3]+ molecule has already been discussed above.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

''compare and contrast the relative contribution of the C and heteroatom to the C-X bond. How do your results relate to the charge distribution just studied?''

The orbitals form C, N, P, S that contribute to the C-X bonds are all roughly sp3 hybridised. However, the orbitals of P and S have a tiny bit of d orbital character because they are third row atoms, which means that 3d orbital is available to them.

From the table above, it can be seen as a general trend that the more electronegative atom between the C and X pair contributes more to the C-X bond. For example, N is more electronegative than C (3.04 vs. 2.55), and hence N contributes more to the C-N bond than C( 66% vs. 34%). This is because the more electronegative atom can attract more electron density than the less electronegative one, i.e. the electron density is more polarised towards the more electronegative atom, and therefore the more electronegative atom contributes more to the C-X bond. From a MO theory's point of view, the orbital that is used to construct the C-X bond of the more electronegative atom is lower in energy than the less electronegative one, which leads to the resulting bonding MO being closer in energy and similar in shape to the orbital of the more electronegative atom. Hence, we get the same conclusion that the more electronegative atom contributes more to the C-X bond.

===Validity of the traditional [N(R4]+ description===

''What does the "formal" positive charge on the N represent in the traditional picture?On what atoms is the positive charge actually located for this cation?''

The concept of formal charge is based on the traditional Lewis structure, in which electron pair is considered to be equally shared between any two bonding atoms regardless of their electronegativities. The definition of formal charge is therefore, the difference between the positive nuclear charge and the total number of electrons of an atom in a given molecule. <ref name="formalcharge" />

Based on this definition, the N atom in [N(R4]+ has a nuclear charge of 7 and total number of electrons of 6, of which 2 belong to the non-bonding inner shell (1s) and 4 are shared with the atoms in the R groups. Therefore, it has a formal charge of +1.

However, because the concept of Lewis structure does not take electronegativities into account, the assignment of +1 charge to the N atom in the case of [N(CH3)4]+ is not correct. The +1 positive charge is actually spread out over all of the H atoms in this cation.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T13:51:31Z

Yz13712: /* [X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

C atoms in all of these structures are negatively charged with a trend that the more electronegative the central atom is the less negatively charged the C atoms are. This is because the more electronegative the central atom is, the stronger the attraction exerted on electron density in the C-X bond from the central atom, which reduces the electron density on the hydrogen atom. However, even when the central atom is the most electronegative N, C is still negatively charged, which is probably due to the 3 electropositive H atoms attached to the C atom.

H atoms in all of these cations are positively charged with similar values. However the more electronegative the central atom is, the less positively charged the H atom is. This is probably due to the size of the central atoms. The least electronegative central atom, P, is the largest one among the three cations, which means that it can spatially accommodate more electron density. Although the electron density is more diffused on P atom, it can suck more electron density from the terminal H atom. S atom is only slightly smaller than the P atom and hence the positive charges on the hydrogens of the S centred cation are just slightly smaller than the hydrogens of the P centred cation, especially for the 6 hydrogens that are closer to the central S atom. Since N is in the second row of the periodic table and hence a significantly smaller atom, the hydrogens of the N centred cation are much less positively charged.

The charge on the central atom is just a measure of its electronegativity. The most electronegative N atom has a negative charge of -0.295, whereas the least electronegative P has a positive charge of 1.667.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

''compare and contrast the relative contribution of the C and heteroatom to the C-X bond. How do your results relate to the charge distribution just studied?''

The orbitals form C, N, P, S that contribute to the C-X bonds are all roughly sp3 hybridised. However, the orbitals of P and S have a tiny bit of d orbital character because they are third row atoms, which means that 3d orbital is available to them.

From the table above, it can be seen as a general trend that the more electronegative atom between the C and X pair contributes more to the C-X bond. For example, N is more electronegative than C (3.04 vs. 2.55), and hence N contributes more to the C-N bond than C( 66% vs. 34%). This is because the more electronegative atom can attract more electron density than the less electronegative one, i.e. the electron density is more polarised towards the more electronegative atom, and therefore the more electronegative atom contributes more to the C-X bond. From a MO theory's point of view, the orbital that is used to construct the C-X bond of the more electronegative atom is lower in energy than the less electronegative one, which leads to the resulting bonding MO being closer in energy and similar in shape to the orbital of the more electronegative atom. Hence, we get the same conclusion that the more electronegative atom contributes more to the C-X bond.

===Validity of the traditional [N(R4]+ description===

''What does the "formal" positive charge on the N represent in the traditional picture?On what atoms is the positive charge actually located for this cation?''

The concept of formal charge is based on the traditional Lewis structure, in which electron pair is considered to be equally shared between any two bonding atoms regardless of their electronegativities. The definition of formal charge is therefore, the difference between the positive nuclear charge and the total number of electrons of an atom in a given molecule. <ref name="formalcharge" />

Based on this definition, the N atom in [N(R4]+ has a nuclear charge of 7 and total number of electrons of 6, of which 2 belong to the non-bonding inner shell (1s) and 4 are shared with the atoms in the R groups. Therefore, it has a formal charge of +1.

However, because the concept of Lewis structure does not take electronegativities into account, the assignment of +1 charge to the N atom in the case of [N(CH3)4]+ is not correct. The +1 positive charge is actually spread out over all of the H atoms in this cation.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T13:51:02Z

Yz13712: /* [X(CH3)y]+ Charge Distribution (NBO) Comparison */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

C atoms in all of these structures are negatively charged with a trend that the more electronegative the central atom is the less negatively charged the C atoms are. This is because the more electronegative the central atom is, the stronger the attraction exerted on electron density in the C-X bond from the central atom, which reduces the electron density on the hydrogen atom. However, even when the central atom is the most electronegative N, C is still negatively charged, which is probably due to the 3 electropositive H atoms attached to the C atom.

H atoms in all of these cations are positively charged with similar values. However the more electronegative the central atom is, the less positively charged the H atom is. This is probably due to the size of the central atoms. The least electronegative central atom, P, is the largest one among the three cations, which means that it can spatially accommodate more electron density. Although the electron density is more diffused on P atom, it can suck more electron density from the terminal H atom. S atom is only slightly smaller than the P atom and hence the positive charges on the hydrogens of the S centred cation are just slightly smaller than the hydrogens of the P centred cation, especially for the 6 hydrogens that are closer to the central S atom. Since N is in the second row of the periodic table and hence a significantly smaller atom, the hydrogens of the N centred cation are much less positively charged.

The charge on the central atom is just a measure of its electronegativity. The most electronegative N atom has a negative charge of -0.295, whereas the least electronegative P has a positive charge of 1.667.

===[X(CH3)y]+ Relative Contribution form C and X to the C-X Bond Comparison Section===
{| class="wikitable"
|+ Relative Contribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| Contribution from X || 66% || 40% || 51%
|-
| Hybridisation of X orbital || 25% s + 75% p|| 25% s + 74% p + 1% d|| 17% s + 82% p + 1% d
|-
| Contribution from C || 34% || 60% || 49%
|-
| Hybridisation of C orbital || 21% s + 79% p || 25% s + 75% p || 20% s + 80% p

|}

''compare and contrast the relative contribution of the C and heteroatom to the C-X bond. How do your results relate to the charge distribution just studied?''

The orbitals form C, N, P, S that contribute to the C-X bonds are all roughly sp3 hybridised. However, the orbitals of P and S have a tiny bit of d orbital character because they are third row atoms, which means that 3d orbital is available to them.

From the table above, it can be seen as a general trend that the more electronegative atom between the C and X pair contributes more to the C-X bond. For example, N is more electronegative than C (3.04 vs. 2.55), and hence N contributes more to the C-N bond than C( 66% vs. 34%). This is because the more electronegative atom can attract more electron density than the less electronegative one, i.e. the electron density is more polarised towards the more electronegative atom, and therefore the more electronegative atom contributes more to the C-X bond. From a MO theory's point of view, the orbital that is used to construct the C-X bond of the more electronegative atom is lower in energy than the less electronegative one, which leads to the resulting bonding MO being closer in energy and similar in shape to the orbital of the more electronegative atom. Hence, we get the same conclusion that the more electronegative atom contributes more to the C-X bond.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T13:50:30Z

Yz13712: /* [X(CH3)y]+ Charge Distribution Comparison Section */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution (NBO) Comparison===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 ; 0.279
|}

C atoms in all of these structures are negatively charged with a trend that the more electronegative the central atom is the less negatively charged the C atoms are. This is because the more electronegative the central atom is, the stronger the attraction exerted on electron density in the C-X bond from the central atom, which reduces the electron density on the hydrogen atom. However, even when the central atom is the most electronegative N, C is still negatively charged, which is probably due to the 3 electropositive H atoms attached to the C atom.

H atoms in all of these cations are positively charged with similar values. However the more electronegative the central atom is, the less positively charged the H atom is. This is probably due to the size of the central atoms. The least electronegative central atom, P, is the largest one among the three cations, which means that it can spatially accommodate more electron density. Although the electron density is more diffused on P atom, it can suck more electron density from the terminal H atom. S atom is only slightly smaller than the P atom and hence the positive charges on the hydrogens of the S centred cation are just slightly smaller than the hydrogens of the P centred cation, especially for the 6 hydrogens that are closer to the central S atom. Since N is in the second row of the periodic table and hence a significantly smaller atom, the hydrogens of the N centred cation are much less positively charged.

The charge on the central atom is just a measure of its electronegativity. The most electronegative N atom has a negative charge of -0.295, whereas the least electronegative P has a positive charge of 1.667.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.

User:Yz13712

2015-02-12T13:24:07Z

Yz13712: /* MO=16 : strong anti-bonding */

==EX3 section==
===BH3:B3LYP/3-21G===

Optimisation log file [[Media:ZYT BH3 OPT CS 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000217 0.000450 YES
RMS Force 0.000105 0.000300 YES
Maximum Displacement 0.000900 0.001800 YES
RMS Displacement 0.000441 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT BH3 OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000410 0.000450 YES
RMS Force 0.000268 0.000300 YES
Maximum Displacement 0.001597 0.001800 YES
RMS Displacement 0.001046 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 321G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 321g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000228 0.000450 YES
RMS Force 0.000111 0.000300 YES
Maximum Displacement 0.000854 0.001800 YES
RMS Displacement 0.000495 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised ammonia molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BH3:B3LYP/6-31G(d,p)===

A better Basis-set

Optimisation log file [[Media:ZYT BH3 OPT CS 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:Zyt Cs 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000203 0.000450 YES
RMS Force 0.000098 0.000300 YES
Maximum Displacement 0.000738 0.001800 YES
RMS Displacement 0.000395 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT_BH3_OPT_Cs_631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT D3H 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| D3h

|[[File:Zyt D3h 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000434 0.000450 YES
RMS Force 0.000284 0.000300 YES
Maximum Displacement 0.001702 0.001800 YES
RMS Displacement 0.001114 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt D3h 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}
Optimisation log file [[Media:ZYT BH3 OPT C1 631G.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:Zyt C1 631g.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000255 0.000450 YES
RMS Force 0.000133 0.000300 YES
Maximum Displacement 0.000920 0.001800 YES
RMS Displacement 0.000598 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised Bh3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT bh3 opt C1 631g.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===GaBr3:B3LYP/LANL2DZ===

optimisation file: {{DOI|10042/193794}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt GaBr3 pp optimisation.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>250</size>
<uploadedFileContents>Zyt GaBr3 pp optimisation.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===BBr3:B3LYP/6-31G(d,p)LANL2DZ (GEN)===

optimisation file: {{DOI|10042/193796}}
{| class="wikitable"
|+
! summary data !! convergence || Jmol
|-

|[[File:Zyt BBr3 GEN.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 0.000024 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BBr3 molecule</title>
<color>lightgrey</color>
<size>250</size>
<uploadedFileContents>ZYT BBr3 GEN opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

==Geometry Comparison==

{| class="wikitable"
|+ geometry data
! !! 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
|}

Summary of the data:
Since both central atoms (B and Ga) in EX3 system are Group 3 element, the symmetry of molecules would remain the same (point group D3h)and the bong angle is exactly 120.0º. However, the changing of ligand and central atom would affect the bond length significantly. Ga atom is much more large than B atom and hence would form a weaker bond due to the shielding effect.

Both H and Br ligands would form single bond with central atom. However the Br atom is larger than H atom, and therefore the orbital overlap for H atom is better than Br atom. Also, Br is more electronegative than H. Hence the bond length of E-Br would be larger than bond length of E-H.

Bond represents the electronic interaction between atoms. The MO theory suggest that electrons are not related to any individual atoms but will move around the whole molecule. The strength of the bond decrease along with the increase of bond length. An ionic bond is generally considered as a strong bond. for example, the ionic bond energy for NaCl is −756 kJ/mol. The single covalent bonds formed by elements from first three row of the periodic table are generally considered as medium bonds. For example, C-C bond has a bond enthalpy of 348 KJ/mol. Hydrogen bonds and other intermolecular interactions (e.g. Van Der Waals force) are often considered as weak bonds and the hydrogen bond is stronger than other intermolecular interactions. The strength of hydrogen bond in H3O is 22 KJ/mol.

The GaussView could only recognize a bond if the distance between the two atoms is smaller than the pre-set value. These values are based on organic molecules, however inorganic molecules will often have longer bonds.

==Frequency Analysis==

===BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT BH3 OPT FREQUENCY.LOG| here]]

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

|[[File:Zyt bh3 frequency.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -7.0630 -7.0272 -0.0278 -0.0010 0.7100 6.6480
Low frequencies --- 1163.0024 1213.1577 1213.1579

</pre>
|}

===Vibrational spectrum for BH3===
{| class="wikitable"
|+
|-
|wavenumber || Intensity || IR active? ||type
|-
|1161
|93
|yes
|bend
|-
|1212
|14
|very slight
|bend
|-
|1212
|14
|very slight
|bend
|-
|2588
|0
|no
|stretch
|-
|2721
|126
|yes
|stretch
|-
|2721
|126
|yes
|stretch
|}

|[[File:Zyt IR spectrum BH3 631g.PNG|300px]]

There are two reasons for why there are fewer vibrational peaks than there are vibrations. The first reason is that some vibration modes does not involve in the change of dipole moment and therefore is IR inactive, for example, the stretch vibrational mode at 2582 cm-1 is IR inactive. The second reason is some of vibrations are degenerated and have exactly the same energy level like two vibrational modes at 1212 cm-1 would only show one peak at IR spectrum.

===GaBr3:B3LYP/LANL2DZ===

Frequency file: {{DOI|10042/193819}}

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

|[[File:Zyt GaBr3 frequency.PNG|300px]]

Energy exactly the same as previous optimization GaBr3 model.

|
<pre>
Low frequencies --- -1.4877 -0.0015 -0.0002 0.0096 0.6540 0.6540
Low frequencies --- 76.3920 76.3924 99.6767

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

|[[File:Zyt IR spectrum GaBr3.PNG|300px]]

Compare and Contrast

Large difference in vibrational frequencies

Since both Ga and Br atoms are larger than B and H atoms indicate a poor orbital overlap and weaker bond between Ga-Br than B-H. Therefore the energy required for stretch or bend the GaBr3 molecule will be much lower than BH3 molecules. Hence the vibrational frequencies of the GaBr3 molecules are much lower than those of the BH3 molecules.

Reordering of the modes

By looking at the vibrational modes of GaBr3 and BH3 in GaussView, both of two molecules contain two types of vibrational modes: one is the umbrella bending motion ( 1163 cm-1 for BH3 and 100 cm-1 for GaBr3) and another one is a pair of equivalent twisted scissoring bending motions( 1213 cm-1 for BH3 and 76 cm-1 for GaBr3). The umbrella motion requires out of plane vibrations of either the central atom or the terminal atoms, where as the twisted scissoring motion requires in-plane vibration of both central and terminal atoms

For BH3, the H atoms are much lighter than the central B atom, therefore, vibrating all of the H atoms requires less energy than vibrating central B atoms and two of the terminal H atoms, which explain the reason why umbrella motion is at a lower frequency.

For GaBr3, the central Ga atom is only slightly lighter than the terminal Br atoms, which makes the umbrella motion less favorable due to the requirement of large change in momentum. Therefore, the umbrella motion for GaBr3 is at a higher frequency.

Form GaussView, we could also see that the umbrella motion for BH3 is dominated by H atoms whereas for GaBr3 is dominated by central Ga atom.

Answer to the questions

The computation method and basis set determine the Potential Energy Surface generated for a molecule. The geometry optimisation is based on the first derivative which locates the minimum on the potential energy surface, where as the frequency calculation is based on the second derivative around the minimum point. If the optimization and frequency analysis are calculated based on different surface, then they are not directly related and there is no point of comparing them.

Frequency analysis (second derivative) can be used to determine whether the stationary point found by the optimization is a minimum or not. If there are any negative frequencies appearing, it means that the molecule is at a saddle point or transition state rather than ground state.

Low frequencies represent the translational and rotational motions of the center of mass of the molecule. Ideally we want the low frequencies to be zero due to the Born-Oppenheimer approximation being made in these calculations, in which we assume the nucleus to be stationary comparing to electrons.

===Molecular Orbitals for BH3===

MO file: {{DOI|10042/193820}}

[[File:MO.PNG|500px]]

There are no significant differences between the real and LCAO MOs, this indicate that the qualitative MO theory is quite fit in predicting the general shapes of the MOs of small molecules.

===NH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:ZYT NH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3 opt.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 BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ZYT NH3 opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:ZYT NH3 FREQ.LOG| here]]

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

|[[File:NH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G BH3 model.

|
<pre>
Low frequencies --- -0.0130 -0.0029 -0.0019 7.1032 8.1046 8.1049
Low frequencies --- 1089.3834 1693.9368 1693.9368

</pre>
|}

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

|[[File:NH3 IR.PNG|300px]]

===NBO Analysis of NH3===

NBO log file: [[Media:ZYT NH3 OPT.LOG| here]]

[[File:NH3 NBO.PNG|300px]]

charge range: from -1.0 to 1.0.

==Association Energy for NH3BH3==

===NH3BH3:B3LYP/6-31G(d,p)===

Optimization log file [[Media:NH3BH3 OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C3v

|[[File:NH3BH3 opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000122 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.000531 0.001800 YES
RMS Displacement 0.000296 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>NH3BH3 Opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

===NH3BH3:B3LYP/6-31G(d,p)===
Frequency file: [[Media:NH3BH3 FREQ.LOG| here]]

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

|[[File:NH3BH3 freq.PNG|300px]]

Energy exactly the same as previous optimization 6-31G NH3BH3 model.

|
<pre>
Low frequencies --- -5.4077 -0.3705 -0.0565 0.0002 0.9580 1.0693
Low frequencies --- 263.2907 632.9543 638.4541

</pre>
|}
===Vibrational spectrum for NH3BH3===
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|263
|0
|no
|bend
|-
|633
|14
|slight
|strecth
|-
|638
|4
|very slight
|bend
|-
|638
|4
|very slight
|bend
|-
|1069
|41
|yes
|bend
|-
|1069
|41
|yes
|bend
|-
|1196
|108
|yes
|bend
|-
|1204
|3
|very slight
|bend
|-
|1204
|3
|very slight
|bend
|-
|1329
|114
|yes
|bend
|-
|1676
|28
|slight
|bend
|-
|1676
|28
|slight
|bend
|-
|2472
|67
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|2532
|231
|yes
|stretch
|-
|3464
|3
|very slight
|stretch
|-
|3581
|28
|slight
|stretch
|-
|3581
|28
|slight
|stretch
|}

[[File:NH3BH3 IR.PNG]]
===Association energy calculation===

E(NH3)=-56.55776873 A.U.

E(BH3)=-26.61532254 A.U.

E(NH3BH3)=-83.22468891 A.U.

ΔE=ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]=-83.22468891 A.U - [-56.55776873 A.U. + -26.61532254 A.U.]= -0.05159746 A.U. =-135 KJ/mol

The disassociation energy of NH3BH3 is obviously greater than hydrogen bonds (22 KJ/mol)and intermolecular attractions, however, it is still considerably smaller than most of the single covalent bond. For example, the B-N bond enthalpy is smaller than typical C-C bond enthalpy(348 KJ/mol), but nearly the same as a N-N single bond (170KJ/mol). Therefore, the B-N bond in NH3BH3 could be more like a medium bond.

===NBO Analysis of ethane and aminoborane===

Ethane NBO log file: [[Media:ETHANE OPT.LOG| here]]

[[File:Nbo ethane.PNG|300px]]

charge range: from -0.687 to 0.687.

Aminoborane NBO log file: [[Media:NH3BH3 NBO.LOG| here]]

[[File:NH3BH3 nbo.PNG|300px]]

charge range: from -0.962 to 0.962.

In ethane, the charge distribution for both C atoms and H atoms are equal(both C atoms is -0.687 and H atoms is 0.220). However, for aminoborane, the charge distribution for two parts are no longer the same: N atom is -0.962, B atom is -0.170 and H atoms net to N is 0.436, H atom next to B is -0.059. These all indicate that the bonds in aminoborane is highly polarized. This fits the character of the aminoborane dative-bond that N atom itself "provides" two electron to B atom. To weaken the N-B bond, we only need to substitute H atoms next to N atom into some electron withdrawing groups (e.g. -OH group) or substitute H atoms next to B atom into some electron donating groups (e.g. -CH3 group).

==Ionic Liquid Project: Part 1==

===[N(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [N(CH3)4]+====

Optimization log file [[Media:N(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:N(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000231 0.001800 YES
RMS Displacement 0.000089 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>N(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)4+ FREQ.LOG| here]]

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

|[[File:N(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0006 -0.0002 0.0007 21.4457 21.4458 21.4458
Low frequencies --- 188.5907 292.6934 292.6934

</pre>
|}

====Vibrational spectrum for [N(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|941
|22
|yes
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1305
|1
|very slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1456
|5
|slight
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|1532
|53
|yes
|bend
|-
|}

[[File:N(CH3)4+ IR.PNG]]

====NBO Analysis of [N(CH3)4]+====

NBO log file: [[Media:N(CH3)4+ NBO.LOG| here]]

[[File:N(CH3)4+ nbo.PNG|300px]]

charge range: from -0.483 to 0.483.

[[File:N(CH3)4+ nbo value.PNG|300px]]

===[P(CH3)4]+:B3LYP/6-31G(d,p)===

====Optimization of [P(CH3)4]+====

Optimization log file [[Media:P(CH3)4+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:P(CH3)4+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000116 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000809 0.001800 YES
RMS Displacement 0.000326 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>P(CH3)4+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [P(CH3)4]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:P(CH3)4+ FREQ.LOG| here]]

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

|[[File:P(CH3)4+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -0.0022 -0.0012 0.0022 24.7170 24.7170 24.7170
Low frequencies --- 160.1015 194.8298 194.8298

</pre>
|}

====Vibrational spectrum for [P(CH3)4]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|271
|2
|very slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|756
|4
|slight
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1013
|78
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1362
|21
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|1481
|26
|yes
|bend
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3064
|5
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|3159
|4
|slight
|stretch
|-
|}

[[File:P(CH3)4+ IR.PNG]]

====NBO Analysis of [P(CH3)4]+====

NBO log file: [[Media:P(CH3)4+ NBO.LOG| here]]

[[File:P(CH3)4+ nbo.PNG|300px]]

charge range: from -1.667 to 1.667.

[[File:P(CH3)4+ nbo value.PNG|300px]]

===[S(CH3)3]+:B3LYP/6-31G(d,p)===

====Optimization of [S(CH3)3]+====

Optimization log file [[Media:S(CH3)3+ OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| TD

|[[File:S(CH3)3+ opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000235 0.001800 YES
RMS Displacement 0.000073 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>S(CH3)3+ OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [S(CH3)3]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:S(CH3)3+ OPT.LOG| here]]

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

|[[File:S(CH3)3+ freq.PNG|300px]]

|
<pre>
Low frequencies --- -7.9007 -7.6403 -7.6370 0.0019 0.0040 0.0093
Low frequencies --- 161.9049 199.6302 199.6302

</pre>
|}

====Vibrational spectrum for [S(CH3)3]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|624
|2
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|704
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|958
|1
|very slight
|bend
|-
|1071
|11
|yes
|bend
|-
|1071
|11
|yes
|bend
|-
|1076
|12
|yes
|bend
|-
|1408
|2
|very slight
|bend
|-
|1464
|10
|yes
|bend
|-
|1464
|10
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1473
|25
|yes
|bend
|-
|1485
|42
|yes
|bend
|-
|3075
|3
|very slight
|stretch
|-
|3075
|3
|very slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3185
|8
|slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|-
|3187
|2
|very slight
|stretch
|}

[[File:S(CH3)3+ IR.PNG]]

====NBO Analysis of [S(CH3)3]+====

NBO log file: [[Media:S(CH3)3+ NBO.LOG| here]]

[[File:S(CH3)3+ nbo.PNG|300px]]

charge range: from -0.917 to 0.917.

[[File:S(CH3)3+ nbo value.PNG|300px]]
===Geometry Comparison of [X(CH3)y]+ molecules===

{| class="wikitable"
|+ geometry data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| r(X-C) Å || 1.51 || 1.82 || 1.82
|-
| r(C-H) Å || 1.09 || 1.09 || 1.09
|-
| θ(C-X-C) degrees(º) || 109.5 || 109.5 || 102.7
|-
| θ(H-C-H) degrees(º) || 110.0 || 109.0 || 109.4 ; 111.1
|-
| θ(X-C-H) degrees(º) || 108.9 || 109.9 || 107.3 ; 110.6
|}

The bond length of C-N is lower than C-P and C-s bond length. This is because both C and N are in the second row of Periodic Table whereas P and S are in the third row. Therefore the C and N atom will have better orbital overlap than C with P or S atom. The bond length between C-H bond did not changed much between three molecules (all are 1.09Å) which means that the change of central atom could not have too much influence on the strength of C-H bond.

The geometry shape of [N(CH3)4]+ molecule and [P(CH3)4]+ molecule are similar for they both have Td symmetry. The 4 methyl groups are all symmetrical due to the ideal bond angle (109.5º) between carbon and central atom. However, the electron distribution of P atom is larger and more diffusive than N atom and therefore would slightly compress the electrons in methyl groups results in lower H-C-H bond angle.

The [S(CH3)3]+ molecule has C3V symmetry and has two different values of H-related bond angle. This is because the total 9 H atoms are in 2 different environment: 6 of them are pointing upward to the central atom and the other 3 atoms (labelled) are pointing downward like the graph below has shown. The lone-pair electrons in S atom will push the 3 methyl groups together results in a significant decrease in C-X-C bond angle.

[[File:S(CH3)3+ H atom.PNG|300px]]
===MOs of [N(CH3)4]+===

====MO=6 : strong bonding====

[[File:MO 1 final.PNG|500px]]

====MO=7 : medium bonding====

[[File:MO 2 final.PNG|500px]]

====MO=11 : weak bonding====

[[File:MO 3 final.PNG|500px]]

====MO=15 : weak anti-bonding====

[[File:MO 4 final.PNG|500px]]

====MO=16 : strong anti-bonding====

[[File:MO 5 final.PNG|500px]]

===[X(CH3)y]+ Charge Distribution Comparison Section===
{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [P(CH3)4]+ !! [S(CH3)3]+
|-
| charge on X || -0.295 || 1.667 || 0.917
|-
| charge on C || -0.483 || -1.060 || -0.846
|-
| charge on H || 0.269 || 0.298 || 0.297 or 0.279*
|}

* The hydrogen atoms in [S(CH3)3]+ have two different values of positive charges due to the existence of two types of equivalent H in this cation. The 6 H atoms pointing upwards (i.e. closer to the central S atom) have more positive charges (0.297), whereas the 3 H atoms pointing away from the central S atom have less positive charges(0.279).

''Compare and contrast the charge distribution across this trio of cations''

C atoms in all of these structures are negatively charged with a trend that the more electronegative the central atom is the less negatively charged the C atoms are. This is because the more electronegative the central atom is, the stronger the attraction exerted on electron density in the C-X bond from the central atom, which reduces the electron density on the hydrogen atom. However, even when the central atom is the most electronegative N, C is still negatively charged, which is probably due to the 3 electropositive H atoms attached to the C atom.

H atoms in all of these cations are positively charged with similar values. However the more electronegative the central atom is, the less positively charged the H atom is. This is probably due to the size of the central atoms. The least electronegative central atom, P, is the largest one among the three cations, which means that it can spatially accommodate more electron density. Although the electron density is more diffused on P atom, it can suck more electron density from the terminal H atom. S atom is only slightly smaller than the P atom and hence the positive charges on the hydrogens of the S centred cation are just slightly smaller than the hydrogens of the P centred cation, especially for the 6 hydrogens that are closer to the central S atom. Since N is in the second row of the periodic table and hence a significantly smaller atom, the hydrogens of the N centred cation are much less positively charged.

The charge on the central atom is just a measure of its electronegativity. The most electronegative N atom has a negative charge of -0.295, whereas the least electronegative P has a positive charge of 1.667.

==Ionic Liquid Project: Part 2==
===[N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)===
====Optimization of [N(CH3)3(CH2OH)]+====

Optimization log file [[Media:N(CH3)3(CH2OH) OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| C1

|[[File:ROH opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000015 0.000450 YES
RMS Force 0.000004 0.000300 YES
Maximum Displacement 0.000428 0.001800 YES
RMS Displacement 0.000112 0.001200 YES

</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>ROH opt.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2OH)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:N(CH3)3(CH2OH) FREQ.LOG| here]]

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

|[[File:ROH freq.PNG|300px]]

|
<pre>
Low frequencies --- -8.4390 -5.0098 -1.0369 -0.0005 -0.0004 0.0009
Low frequencies --- 131.1078 213.4644 255.7166

</pre>
|}

====Interesting aspect of the structure of [N(CH3)3(CH2OH)]+====
During the optimisation of [N(CH3)3(CH2OH)]+, another structure came out initially, with O-H bond being antiperiplanar to the C-N bond, of which the C is the OH directly attached to. Despite the fact that this structure has a CV symmetry, which is higher in symmetry than the structure presented above (C1, further frequency analysis showed that this structure is not a minimum as it has a imaginary frequency.

The reason why [N(CH3)3(CH2OH)] prefers a low symmetry structure may be explained by the attraction between O atom and 2H atoms on adjacent carbon atoms (The two H atoms that are pointing in the same direction as the O atom on adjacent C atoms). The maximum attraction between non-bonded H and O typically occurs at 2.62 Å, estimated in the basis of their Van Der Waals's radii.<ref name="VDR" />

In the CV symmetry structure, the distances between O and two H are both 2.41 Å, whereas these distances for the C1 symmetry structure are 2.55 and 2.46 Å. Therefore, clearly that the attraction between non-bonded O and H in the low symmetry structure is stronger and hence it is lower in energy. In fact, if we examine the imaginary frequency of the high symmetry structure, it corresponds to a bending motion that moves the hydroxyl H to the position that it sits in the low symmetry structure.

====Vibrational spectrum for [N(CH3)3(CH2OH)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|131
|5
|slight
|bend
|-
|213
|3
|very slight
|bend
|-
|256
|29
|yes
|bend
|-
|267
|1
|very slight
|bend
|-
|342
|51
|yes
|bend
|-
|355
|4
|very slight
|bend
|-
|393
|28
|yes
|bend
|-
|434
|4
|very slight
|bend
|-
|449
|4
|very slight
|bend
|-
|552
|2
|very slight
|bend
|-
|736
|22
|yes
|bend
|-
|839
|96
|yes
|bend
|-
|931
|22
|yes
|bend
|-
|982
|12
|yes
|bend
|-
|1033
|20
|yes
|bend
|-
|1122
|38
|yes
|bend
|-
|1133
|7
|slight
|bend
|-
|1184
|91
|yes
|bend
|-
|1219
|8
|slight
|bend
|-
|1276
|6
|slight
|bend
|-
|1289
|2
|very slight
|bend
|-
|1330
|19
|yes
|bend
|-
|1397
|17
|yes
|bend
|-
|1433
|3
|very slight
|bend
|-
|1445
|7
|slight
|bend
|-
|1452
|9
|slight
|bend
|-
|1496
|5
|slight
|bend
|-
|1501
|3
|very slight
|bend
|-
|1504
|1
|very slight
|bend
|-
|1514
|26
|yes
|bend
|-
|1521
|33
|yes
|bend
|-
|1530
|17
|yes
|bend
|-
|1540
|51
|yes
|bend
|-
|3074
|9
|slight
|stretch
|-
|3085
|2
|very slight
|stretch
|-
|3088
|2
|very slight
|stretch
|-
|3095
|1
|very slight
|stretch
|-
|3147
|4
|very slight
|stretch
|-
|3184
|1
|very slight
|stretch
|-
|3189
|1
|very slight
|stretch
|-
|3825
|105
|yes
|stretch
|}

[[File:ROH IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2OH)]+====
Population log file [[Media:N(CH3)3(CH2OH) NBO.LOG | here]]

[[File:ROH NBO.PNG]]

charge range -0.757 to 0.757

[[File:ROH NBO value.PNG]]

===[N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p) level===
====Optimization of [N(CH3)3(CH2CN)]+====

Optimization log file [[Media:RCN OPT.LOG| here]]
{| class="wikitable"
|+
! geometry!! summary data || convergence || Jmol
|-

| Cs

|[[File:RCN opt.PNG|300px]]

|
<pre>
Item Value Threshold Converged?
Maximum Force 0.000250 0.000450 YES
RMS Force 0.000057 0.000300 YES
Maximum Displacement 0.001338 0.001800 YES
RMS Displacement 0.000490 0.001200 YES
</pre>
|
<jmol><jmolApplet>
<title>optimised BH3 molecule</title>
<color>lightgrey</color>
<size>200</size>
<uploadedFileContents>RCN OPT.mol2</uploadedFileContents>
</jmolApplet></jmol>
|}

====Frequency of [N(CH3)3(CH2CN)]+:B3LYP/6-31G(d,p)====
Frequency file: [[Media:RCN FREQ.LOG| here]]

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

|[[File:RCN freq.PNG|300px]]

|
<pre>
Low frequencies --- -3.6828 0.0004 0.0005 0.0011 2.7427 3.8837
Low frequencies --- 91.8731 153.9653 212.1350

</pre>
|}

====Vibrational spectrum for [N(CH3)3(CH2CN)]+====
{| class="wikitable"
|+
|-
|wavenumber (cm-1) || Intensity || IR active? ||type
|-
|92
|6
|slight
|bend
|-
|154
|9
|slight
|bend
|-
|328
|1
|very slight
|bend
|-
|436
|1
|very slight
|bend
|-
|571
|2
|very slight
|bend
|-
|895
|28
|yes
|bend
|-
|911
|20
|yes
|bend
|-
|963
|14
|yes
|bend
|-
|990
|20
|yes
|bend
|-
|1008
|2
|very slight
|bend
|-
|1140
|1
|very slight
|bend
|-
|1259
|1
|very slight
|bend
|-
|1333
|3
|very slight
|bend
|-
|1395
|8
|slight
|bend
|-
|1454
|8
|slight
|bend
|-
|1455
|8
|slight
|bend
|-
|1475
|3
|very slight
|bend
|-
|1495
|3
|very slight
|bend
|-
|1503
|3
|very slight
|bend
|-
|1519
|34
|yes
|bend
|-
|1521
|47
|yes
|bend
|-
|1532
|61
|yes
|bend
|-
|2385
|8
|slight
|stretch
|-
|3087
|1
|very slight
|stretch
|-
|3144
|2
|very slight
|stretch
|}

[[File:RCN IR.PNG|500px]]

====NBO analysis for [N(CH3)3(CH2CN)]+====
Population log file [[Media:RCN NBO.LOG | here]]

[[File:RCN NBO.PNG]]

charge range -0.489 to 0.489

[[File:RCN NBO value.PNG]]

===Charge distribution comparison between [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+===

{| class="wikitable"
|+ charge distribution data
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| charge on N || -0.295 || -0.322 || -0.289(central), -0.186(CN)
|-
| charge on C || -0.483 || -0.494 ~ -0.491(CH3), 0.088(CH2OH) || -0.385 ~ -0.489(CH3), 0.209((CN)
|-
| charge on O || N/A || -0.725 || N/A
|-
| charge on H || 0.269 || 0.266 ~ 0.282(CH3), 0.237 ~ 0.249(CH2OH), 0.521(CH2OH) || 0.269 ~ 0.282(CH3), 0.309(CH2CN)
|}

''OH is an electron donating group and CN is an electron withdrawing group, what effect have these groups had on the charge distribution?''

From the charge distribution data, it is easy to discover that OH has pushed electron density across the ammonium cation, which increases the negative charge on the central N atom and most of the carbon atom apart from the one which it is directly attached to. The positive charge on the H atoms in [N(CH3)3(CH2OH)] has also been decreased apart from the hydroxyl H. Generally, the closer the H atom to the OH group, the less positive the H is.

On the other hand, the CN group has significantly withdrawn electron density from both the central N atom and most of the carbon atom apart from the one which it is directly attached to. As a result, the negative charge on both the central N and C atoms has decreased comparing to the reference [N(CH3)4]+. The positive charges on the H atoms in [N(CH3)3(CH2CN)]+ have also increased and the amount of increases have a negative correlation with the distance between the H and the CN.

===HOMO and LUMO comparison===
{| class="wikitable"
|+ HOMO and LUMO graph
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO || [[File:LY_NCH34_HOMO.jpg|300px]] || [[File:LY_NCH33CH2OH_HOMO.jpg|300px]] || [[File:LY_NCH33CH2CN_HOMO.jpg|300px]]
|-
| LUMO || [[File:LY_NCH34_LUMO.jpg|300px]] || [[File:LY_NCH33CH2OH_LUMO.jpg|300px]] || [[File:LY_NCH33CH2CN_LUMO.jpg|300px]]
|}

'''Note:''' The HOMO of [N(CH3)4]+ is triply degenerate.

{| class="wikitable"
|+ HOMO and LUMO energy
! !! [N(CH3)4]+ !! [N(CH3)3(CH2OH)]+ !! [N(CH3)3(CH2CN)]+
|-
| HOMO (Hartree) || -0.57934 || -0.48763 || -0.50047
|-
| LUMO (Hartree) || -0.13303 || -0.12459 || -0.18183
|-
| HOMO-LUMO gap (KJ•mol-1) || 1172 || 953 || 837
|}

''how has the shape of the orbitals changed?

''has the energy of these orbitals moved?

''has the HOMO-LUMO gap changed in size?

''what chemical impact could these changes have?

The HOMO of [N(CH3)4]+ is triply degenerate due to the tetrahedral geometry of the cation. By introducing the OH or CN, the symmetries of the HOMOs are broken and HOMO orbitals are more localised and contracted as well. The latter is due to the existence of the electronegative O and N which can suck in electron densities. The HOMO of [N(CH3)3(CH2CN)]+ is actually more localised than [N(CH3)3(CH2OH)]+, probably due to the electron withdrawing nature of CN. This effect is more obvious on the LUMO orbitals. The LUMO of [N(CH3)3(CH2CN)]+ is significantly more contracted than that of the [N(CH3)3(CH2OH)]+.

The energies of HOMO orbitals have increased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ due to the occurrence of nodal planes in these two cations, which indicates an increased amount of anti-bonding interactions.

On the other hand, the energies of LUMO orbitals have increased for both [N(CH3)3(CH2OH)]+ but decreased for [N(CH3)3(CH2CN)]+, which means that [N(CH3)3(CH2CN)]+ is more susceptible to nucleophilic attack than [N(CH3)3(CH2OH)]+. This is consistent with our chemical intuitions as CN is general a better leaving group than OH.

The LUMO-HOMO gap has also decreased for both [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+, which means that both of them are more liable to photo and thermal exaction than [N(CH3)4]+.