File:Isomer 3 -11.gif

2013-11-22T13:37:12Z

Yz8711:

File:Isomer 1 -18.gif

2013-11-22T13:37:12Z

Yz8711:

2013-11-22T12:11:34Z

Yz8711: /* Computational Chemistry Inorganic module Lab */

==Computational Chemistry Inorganic module Lab==

===Optimising a Molecule of BH3===

Create a BH3 molecule, set one B-H bond to 1.53 angstrom, one B-H bond to 1.54 angstrom, and the third B-H bond to 1.55 angstrom.

====BH3 3-21G optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
</pre>

Full BH3 3-21G optimisation log file is liked to [[media:Yiyun bh3 opt2.LOG| here]].

'''Table 1. BH3 3-21G Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.94Å||120.00°
|}

'''BH3 3-21G optimisation summary'''
<pre>
BH3 optimisation
File Name = yiyun_bh3_opt2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 3-21G
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.46226429 a.u.
RMS Gradient Norm = 0.00008851 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.
</pre>

[[image:BH3 321g optimisation.PNG|left|700px|center|thumb|Figure 1.total energy curve and RMS gradient]]

 
These two graphs illustrate the process of BH3 3-21G optimisation, while the first shows the energy of the molecule at each step and the second gives the gradient of optimisation of each step of optimisation. When the gradient shows a value which is very close to zero, it means the optimisation is completed.

===Using a better basis set===

====BH3 6-31G(d,p) optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
</pre>

Full BH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN BH3 OPT2 631GDP.LOG| here]].

'''Table 2. BH3 6-31G(d,p) Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.19Å|| 1.196Å<ref name="BH distance">Peng, Bin; Li, Qian-Shu; Xie, Yaoming; Bruce King, R.; Schaefer, Henry F. III
Chemical Physics, 2009 , vol. 356, p. 171 - 176;{{DOI|10.1016/j.chemphys.2008.10.050}}</ref>||120.00°
|}

'''BH3 6-31G(d,p) optimisation summary'''
<pre>
BH3 optimisation 631g
File Name = yiyun_bh3_opt2_631gdp
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532360 a.u.
RMS Gradient Norm = 0.00000707 a.u.
Imaginary Freq =
Dipole Moment = 0.0001 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 41.0 seconds.
</pre>

'''Table 3. Total energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 3-21G'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 6-31G(d,p)'''
|-
| -26.46226429 a.u.||-26.61532360 a.u.
|}

===Using pseudo-potentials and larger basis sets===

====GaBr3 optimisation====

<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
Predicted change in Energy=-1.282692D-12
Optimization completed.
</pre>

Full GaBr3 LanL2DZ optimisation log file is liked to [[media:GaBr3 opt lan.log| here]].

'''GaBr3 LanL2DZ optimisation summary(HPC)'''
<pre>
GaBr3 optimisation
File Name = GaBr3_opt_lan
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000016 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 21.6 seconds.
</pre>

"D-space" link : {{DOI|10042/26121}}

'''Table 4. GaBr3 optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-Ga-Br bond angle'''
|-
| 2.35Å||2.239±0.007Å (at 357K)<ref name="GaBr distance">Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998 , vol. 445, # 1-3 p. 139 - 148; {{DOI|10.1016/S0022-2860(97)00420-1}}</ref>||120.00°
|}

The Gaussian calculated Ga-Br bond distance 2.35 Å is longer than the literature value 2.239±0.007 Å. The gaussian optimised structure is based on gas-phase hypothesis, while the literature value might be figured out through experiment. Therefore, interactions like solid state forces or crystal packing forces will distort the molecule by shrinking the Ga-Br bond distance.

===Using a mixture of basis-sets and psuedo-potentials===

====BBr3 Gen optimisation====

===Reference===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-2.171373D-09
Optimization completed.
</pre>

Full BBr3 Gen optimisation log file is liked to [[media:BBr3 opt.log| here]].

'''BBr3 Gen optimisation summary'''
<pre>
BBr3 optimisation 631g
File Name = BBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43644900 a.u.
RMS Gradient Norm = 0.00000974 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 36.4 seconds.
</pre>

"D-space" link : {{DOI|10042/26129}}

'''Table 5. BBr3 Gen Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-B-Br bond angle'''
|-
| 1.93Å||1.8985Å<ref name="BBr distance">Santiso-Quinnones, Gustavo; Krossing, Ingo Zeitschrift fuer Anorganische und Allgemeine Chemie, 2008 , vol. 634, p. 704 - 707; {{DOI|10.1002/zaac.200700510}}</ref>||120.00°
|}

===Structure Comparison===

====Analysing results====

'''Table. Bond distance comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''BH3'''
| align="center" style="background:#0D4F8B; color: white;"|'''BBr3'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3'''
|-
| Bond distance||1.19Å||1.93Å||2.35Å
|-
| Lit. Bond distance||1.196Å||1.8985Å||2.239Å
|}

By comparing the molecule with same central element and different ligands, take BH3 and BBr3 as an example. The Bond distance is much longer for Boron bond with larger ligand Br compared with Boron bond with H, with 1.196Å and 1.8985Å respectively. The reason to cause such a difference is due to that B-Br has larger electronegativity difference than B-H . Therefore, the polarity bewteen Boron and Br is much strong than the one between Boron and H. This can cause unequal sharing of electrons between atoms, which weaken the bond. (Electronegativity: B=2.04 H=2.20 Br=2.96) Br has an atomic number 17, which is larger compared with H with 1 atomic number. This leads to that Br has a large atomic radius and low positive charge density, therefore poor orbital overlap. The valence shell of Br [[Ar] 4s2 3d10 4p5] is '''p''' orbital, while the valence shell of H is '''s''' orbital.
 
By comparing BBr3 with GaBr3, the bond distance of GaBr3 is slightly larger than BBr3. The same reason to cause such a differece is due to the electronegativity difference for Ga-Br is larger than B-Br, therefore leads to a more unequal sharing of electrons, which weaken the bond.(Electronegativity: B=2.04 Ga=1.81 Br=2.96) Meanwhile, Gallium has a larger atomic number 31[[Ar] 3d10 4s2 4p1], compared with boron with atomic number 5[[He] 2s2 2p1]. Therefore, Gallium has a larger atomic radius and poor positive charge density, leads to the poorer orbital overlap with Br and longer the bond.
 
Yes, the bond does exist! The reason why in some structures don't have any bonds is because that the distance exceeds the pre-defined value set in gaussview. The gaussview draws bonds based on a distance critera!
 
There are three types of bonds, which are covalent bond(formed by sharing electrons), ionic bond(formed by transferring the electrons) and metallic bond(formed by the delocalised electrons gathering at the positive charged metal ion surface).

===Frequency Analysis===

====frequency analysis for BH3====

<pre>
Low frequencies --- -0.9382 -0.8426 -0.0054 5.8717 11.7883 11.8256
Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.909158D-10
Optimization completed.
</pre>

Full BH3 6-31G(d,p) frequency log file is liked to [[media:YIYUN BH3 FREQ.LOG| here]].

'''BH3 6-31G(d,p) frequency summary'''

<pre>
BH3 freq
File Name = YIYUN_BH3_freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = 0.00000284 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 23.0 seconds.
</pre>

====Animating the vibrations====

'''Table'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''form of vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''symmetry D3h point group'''
|-
| 1||[[image:1163.gif|center|250px|center]]Three hydrogen bent in a same direction |||1163||92.55|| A2"
|-
| 2||[[image:1213.gif|center|250px|center]] Two hydrogen bent towards a symmetric direction while the other remains constant||1213.18||14.06|| degenerated E'
|-
| 3||[[image:1213(large).gif|center|250px|center]] Three hydrogen bent towards random directions without any correlation ||1213.19||14.06|| degenerated E'
|-
| 4||[[image:2582.gif|center|250px|center]] Three hydrogen stretch symmetrically||2582.27||0|| totally symmetric A'1
|-
| 5||[[image:2715.gif|center|250px|center]] Two hydrogen stretch in opposite directions against each other (one move towards Boron, the other moves away Boron), the left hydrogen remains constant ||2715.44||126.33|| degenerated E'
|-
| 6||[[image:2715(large).gif|center|250px|center]]Two hydrogen stretch in the same direction against the third hydrogen (two move towards Boron, the other moves away Boron)||2715.45||126.32|| degenerated E'
|}

'''BH3 IR spectrum'''

[[image:BH3 IR spectrum.svg|650px|center|thumb|Figure 1.BH3 IR spectrum]]

From the spectra, it only shows three peaks. However, in the table above, there are six vibration frequencies come out. The reason is that there are two pairs of degenerated energy levels which give the same frequency, with 1213 cm-1 and 2715 cm-1 separately. What's more, the total symmetric energy level A'1 is IR inactive. Therefore, there are only there peaks come out.

===GaBr3 Analysis===

====frequency analysis for GaBr3====

<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
</pre>

Full GaBr3 LanL2DZ frequency log file is liked to [[media:GaBr3freqHPC.log| here]].

'''GaBr3 LanL2DZ frequency summary'''
<pre>
GaBr3 freq
File Name = GaBr3freqHPC
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000011 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 14.2 seconds.
</pre>

"D-space" link : {{DOI|10042/26130}}

'''GaBr3 IR spectrum'''
[[image:GaBr3 IR spectrum.svg|650px|center|thumb|Figure 1.GaBr3 IR spectrum]]

'''Table. BH3 and GaBr3 vibrational frequency comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 Frequency /cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 symmetry D3h point group'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 symmetry D3h point group'''
|-
| 1||1163||92.55||A2"||76.37||3.34||E'
|-
| 2||1213.18||14.06||E'||76.38||3.34||E'
|-
| 3||1213.19||14.06||E'||99.7||9.22||A2"
|-
| 4||2582.27||0||A'1||197.34||0||A1'
|-
| 5||2715.44||126.33||E'||316.18||57.07||E'
|-
| 6||2715.45||126.32||E'||316.19||57.07||E'
|}

Both BH3 and GaBr3 molecule has a D3h point group. That is why they both show six vibration frequencies with two pairs of degenerated e' energy levels, one totally symmetric a1' energy level and one a2" energy level. It also explains why only three peaks shows in IR spectrum. The obvious difference is that GaBr3 has a larger frequency value in general compared with BH3. The reason is that BH bond is more rigid compared with GaBr bond. It is also due to the shorter bond length which refers to larger force constant for BH bond. Therefore, more vibrational energy required to cause a stretch or bent to the structure, result in high vibrational frequency.

Within each molecule, six vibrational frequencies could be allocated into two groups. One is '''bent''' structure and the other is '''stretch''' structure. Take BH3 as an example, according to the MO diagram shown above, frequencies with value 1163-1; 1213.18-1; 1213.19-1 are recognised as '''bent''' structure while the other three left are '''stretch ''' structure. The '''stretch ''' structure shows higher vibrational frequency than '''bent''' structure. The reason might be that changing bond length requires a higher vibrational energy than changing the bond angle does.

It is meaningless to compare the energies with different basis set (or pseudo-potentials) due to that total energy calculation is highly depend on the quality of basis set. The energy difference would be quite large if we using the different basis set to compare, due to that the energy is in unit '''a.u'''. (1 a.u.= 2625kJ/mol)

By carrying out a frequency analysis, we could make sure that we find out the optimised structure with minimal energy through the vibrational frequency and the IR correlated spectrum.

"low frequency" refers to the motions of the center of mass of the molecule. Take BH3 as an example, low frequencies here represent -6 by using the formula '''3N-6 ''', where N is the number of atoms.

===Molecular Orbital of BH3===

'''BH3 energy summary'''
<pre>
BH3 energy
File Name = BH3_631g_energyHPC
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 15.9 seconds.
</pre>
"D-space" link : {{DOI|10042/26135}}

[[image:BH3 MOzyy.gif|left|600px|center|thumb|Figure 2.BH3 molecular orbital diagram]]

'''Table. MO diagrams'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''Energy level'''
| align="center" style="background:#0D4F8B; color: white;"|'''MO diagram'''
|-
| degenerated antibonding 2e'||[[image:2e' 1.JPG|left|150px|center]][[image:2e' 2.JPG|left|150px|center]]
|-
| antibonding 3a1'(LUMO orbital)||[[image:3a1'.JPG|left|150px|center]]
|-
| non-bonding 1a2''||[[image:2a1''.JPG|left|150px|center]]
|-
| degenerated bonding 1e'||[[image:1e' 1.JPG|left|150px|center]][[image:1e' 2.JPG|left|150px|center]]
|-
| bonding 2a1'||[[image:2a1'.JPG|left|150px|center]]
|}

Answer the following questions:

What does this say about the accuracy and usefulness of qualitative MO theory?

Real MOs include the consideration of the electronic density distribution which makes it more diffuse compared with the LCAO MOs as we can see from the diagrams above. The LCAO MOs only shows the clear atomic orbital interactions.

===NBO Analysis===

'''NH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.629718D-09
Optimization completed.
</pre>

Full NH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN NH3 OPT 631G.LOG| here]].

'''NH3 6-31G(d,p) optimisation summary'''
<pre>
NH3 optimisation
File Name = YIYUN_NH3_OPT_631G
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 1 minutes 6.0 seconds.
</pre>

'''NH3 6-31G(d,p) frequency'''
<pre>
Low frequencies --- -7.2856 -7.2001 -7.1997 -0.0020 0.0018 0.0124
Low frequencies --- 1089.2799 1693.9186 1693.9186
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.315803D-10
Optimization completed.
</pre>

Full NH3 6-31G(d,p) frequency log file is liked to [[media:NH3 freq3.log| here]].

'''NH3 6-31G(d,p) frequency summary'''
<pre>
NH3 frequency
File Name = NH3_freq3
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776873 a.u.
RMS Gradient Norm = 0.00000237 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8464 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 22.5 seconds.
</pre>

"D-space" link : {{DOI|10042/26151}}

'''NH3 IR spectrum'''

'''NH3 IR energy summary'''
<pre>
NH3 energy
File Name = NH3_energy
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 32.2 seconds.
</pre>

'''NH3 charge distribution diagrams''
[[image:NH3 charge distribution.PNG|left|200px|center|thumb| charge range:-1.0 to +1.0 ]]

[[image:NH3 charge number.PNG|center|200px|thumb| NBO NH3 with specific charge number]]
 
Red color means highly electronegative, while green color refers to electropositive. The nitrogen has a negative charge of -1.125 and the hydrogen has a positive charge of 0.375. The molecule is neutral due to that the negative charge and the sum of the three positive charges are cancelled out.
 

===Association energies: Ammonia-Borane===

'''NH3BH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000024 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.746365D-11
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) optimisation log file is liked to [[media:NH3BH3 OPT 631G 2.LOG| here]].

'''NH3BH3 6-31G(d,p) optimisation summary'''
<pre>
NH3BH3 opt
File Name = NH3BH3_OPT_631G_2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468911 a.u.
RMS Gradient Norm = 0.00000122 a.u.
Imaginary Freq =
Dipole Moment = 5.5647 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

'''NH3BH3 6-31G(d,p) frequency'''

<pre>
Low frequencies --- -5.3030 -0.3083 -0.0451 -0.0011 1.2000 1.2747
Low frequencies --- 263.2955 632.9608 638.4638
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000024 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.117730D-10
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) frequency log file is liked to [[media:NH3BH3 FREQ.LOG| here]].

'''NH3BH3 6-31G(d,p) frequency summary'''

<pre>
NH3BH3 freq
File Name = NH3BH3_FREQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468909 a.u.
RMS Gradient Norm = 0.00000139 a.u.
Imaginary Freq = 0
Dipole Moment = 5.5646 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

'''Table. Frequency energy comparison( Basis set = 6-31G (d,p) )'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(BH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3BH3)'''
|-
| -56.55776873 a.u.||-26.61532363 a.u.||-83.22468909 a.u.
|}

'''Association energy'''
<pre>
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22468909 - [-56.55776873 + (-26.61532363)]
= -0.05159673 a.u.
= -135.47 kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

'''Dissociation energy = 135.47 kJ/mol''' The dissociation energy is positive, therefore it is an endothermic process. It indicates that Ammonia-Borane is more stable.

===Mini Projcet : Lewis acid and base===

===4 possible isomers of Al2Cl4Br2 Optimisation===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Name||2br inmid_opt||1BR INMID_OPT_gen||br up down opt||2br at top_opt
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm||0.00000188||0.00001352||0.00001372||0.00000660
|-
| Imaginary Freq||||||||
|-
| Dipole Moment||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time||0 days 0 hours 7 minutes 23.6 seconds.|| 0 days 0 hours 1 minutes 39.0 seconds.|| 0 days 0 hours 5 minutes 42.7 seconds.||0 days 0 hours 8 minutes 37.5 seconds.
|-
| D-space link || {{DOI|10042/26227}}|| {{DOI|10042/26261}}|| {{DOI|10042/26343}}|| {{DOI|10042/26231}}
|-
| full opt. log file ||[[media:2br inmid opt.log| Isomer 1]] || [[media:1BR INMID OPT gen.LOG| Isomer 2]]||[[media:Br up down opt.log| Isomer 3]] ||[[media:2br at top opt.log| Isomer 4]]
|}

Base on the knowledge we learnt before, the real point group base on the isomer structure shows below:

'''Table. Real point group and symmetry elements of four isomers'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||[[image:2br in mid -sym.PNG|left|200px|center|]] ||[[image:1br in mid -sym.PNG|left|200px|center|]] || [[image:Br up and down -sym.PNG|left|200px|center|]]||[[image:2br at top- sym.PNG|left|200px|center|]]
|-
| symmetry elements ||E,C2(z),C2 (y),C2(x,)i,σ(xy),σ(xz),σ(yz)||E||E,C2(z),i,σh||E,C2(z),σv(xz),σv(yz)
|-
| Real point group ||D2h||C1||C2h||C2v
|}

'''Isomer 1 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.944095D-10
Optimization completed.
</pre>

'''Isomer 2 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000548 0.001800 YES
RMS Displacement 0.000196 0.001200 YES
Predicted change in Energy=-2.150173D-08
Optimization completed.
</pre>

'''Isomer 3 optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001062 0.001800 YES
RMS Displacement 0.000483 0.001200 YES
Predicted change in Energy=-1.142040D-08
Optimization completed.
</pre>

'''Isomer 4 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000833 0.001800 YES
RMS Displacement 0.000305 0.001200 YES
Predicted change in Energy=-2.399764D-08
Optimization completed.
</pre>

===AlCl2Br monomer optimisation===

<jmol><jmolApplet><title>Alcl2br freq.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>Alcl2br freq.mol2</uploadedFileContents></jmolApplet></jmol>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984520D-08
Optimization completed.
</pre>

Full AlCl2Br monomer gen optimisation log file is liked to [[media:AlCl2Br opt gen.log| here]].

'''AlCl2Br monomer gen optimisation summary'''

<pre>
AlCl2Br opt
File Name = AlCl2Br opt_gen
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004196 a.u.
Imaginary Freq =
Dipole Moment = 0.1075 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 17.3 seconds.
</pre>

===AlCl2Br monomer frequency analysis===

<pre>
Low frequencies --- 0.0029 0.0030 0.0044 1.3628 3.6408 4.2614
Low frequencies --- 120.5042 133.9180 185.8952
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000082 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000975 0.001200 YES
Predicted change in Energy=-1.813492D-07
Optimization completed.
</pre>

Full AlCl2Br monomer frequency log file is liked to [[media:Alcl2br freq.log| here]].

'''AlCl2Br monomer gen frequency summary'''

<pre>
AlCl2Br freq
File Name = Alcl2br freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004201 a.u.
Imaginary Freq = 0
Dipole Moment = 0.1075 Debye
Point Group = C2V
Job cpu time: 0 days 0 hours 0 minutes 37.4 seconds.
</pre>

[[image:Alcl2br IR.svg|650px|center|thumb|Figure 1.AlCl2Br monomer IR]]

'''Table. Opt Energy comparison of for isomers'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/ a.u.'''
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/kJ/mol'''
| align="center" style="background:#0D4F8B; color: white;"|'''related'''
| align="center" style="background:#0D4F8B; color: white;"|'''Energy difference compared to the lowest one/kJ/mol'''
|-
| Isomer 1||-2352.40630798||-6176240.41||highest||26.28
|-
| Isomer 2||-2352.41109948||-6176252.99||||13.70
|-
| Isomer 3||-2352.41631610||-6176266.69||lowsest||0
|-
| Isomer 4||-2352.41626680||-6176266.56||||0.13
|}

Isomer 3, with two terminal Br at diagonal position, has the lowest energy, indicating the most stable conformer. Isomer 4, with two terminal Br at symmetric position, has the second lowest energy. However, the energy difference is quite small with a value of 0.13kJ/mol only. For those isomers with at least one Br connected at bridged position, by comparing to the most stable conformer(non-Br bridged isomer), it shows a quite large energy gap between them. Isomer 1, with two bridged Br in mid, has the highest energy, indicating the least stable conformer. Isomer 2, with only one Br at bridged position, shows a half value of the difference between the two-Br bridged isomer and non-Br bridged conformer.

The reason to cause such a energy gap can be explained by the difference in overlap between orbitals. Al, Cl and Br have electronic configurations with [[Ne] 3s2 3p1], [[Ne] 3s2 3p5] and [[Ar] 4s2 3d10 4p5] respectively. The 3p-3p (Al-Cl bridged bond)orbital overlap is more stable than 3p-4p(Al-Br bridge bond)orbital overlap, therefore isomer 3 is most stable. Meanwhile, the steric effect would also be a factor to be considered why Cl is more stable at bridged position other than Br.

===Dissociation energy for the lowest energy conformer(Isomer 3)===

'''Opt energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''AlCl2Br'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
|-
| -2352.41631610 a.u.||-1176.19013679 a.u.
|}

<pre>
ΔE= [(E(AlCl2Br)*2)-E(Al2Cl4Br2)]
= [(-1176.19013679*2) - (-2352.41631610)]
= 0.03604252a.u.
= 94.63kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

The dissociation energy computed above is a positive value which indicates it is an endothermic process. Therefore, the product is more favourable than the monomer.

By comparing the monomer with the product dimer, the later one is more stable. It can be explained by that the monomer has only 6 bonded electron in the center Al, which shows a higher electron deficiency than the bridged dimer with 8 electrons in each Al center.

===4 possible isomers of Al2Cl4Br2 Frequency analysis===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FREQ||FREQ||FREQ||FREQ
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)/ a.u.||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm/ a.u.||0.00000188||0.00001354||0.00001368||0.00000657
|-
| Imaginary Freq||||||||
|-
| Dipole Moment/Debye||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time|| 0 days 0 hours 1 minutes 11.9 seconds.|| 0 days 0 hours 3 minutes 31.5 seconds.|| 0 days 0 hours 2 minutes 30.3 seconds.|| 0 days 0 hours 1 minutes 40.9 seconds.
|-
| D-space link||{{DOI|10042/26347}}||{{DOI|10042/26348}}||{{DOI|10042/26349}}||{{DOI|10042/26230}}
|-
| full freq. log file ||[[media:2br inmid freq.log| Isomer 1]] || [[media:1 br in mid freq.log| Isomer 2]]||[[media:Br up down freq.log| Isomer 3]] ||[[media:2br at top freq.log| Isomer 4]]
|}

'''Isomer 1 frequnency'''
<pre>
Low frequencies --- -5.1748 -5.0353 -3.1463 -0.0055 -0.0053 -0.0051
Low frequencies --- 14.8261 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.736206D-10
Optimization completed.
</pre>

[[image:2br inmid IR.svg|650px|center|thumb|Figure 1.Isomer 1 IR]]

'''Isomer 2 frequnency'''
<pre>
Low frequencies --- -2.3182 -0.0011 0.0024 0.0034 1.0656 3.0876
Low frequencies --- 17.1031 55.9263 80.0668
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000887 0.001800 YES
RMS Displacement 0.000381 0.001200 YES
Predicted change in Energy=-3.842255D-08
Optimization completed.
</pre>

[[image:1br in mid IR.svg|650px|center|thumb|Figure 1.Isomer 2 IR]]

'''Isomer 3 frequnency'''
<pre>
Low frequencies --- 0.0034 0.0034 0.0035 1.8920 1.9704 3.9624
Low frequencies --- 18.0988 49.0858 72.9223
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000040 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.001356 0.001800 YES
RMS Displacement 0.000593 0.001200 YES
Predicted change in Energy=-1.805357D-08
Optimization completed.
</pre>

[[image:Up and down IR.svg|650px|center|thumb|Figure 1.Isomer 3 IR]]

'''Isomer 4 frequnency'''
<pre>
Low frequencies --- -4.2528 -2.3928 -0.0052 -0.0050 -0.0043 1.2845
Low frequencies --- 17.1623 50.9093 78.5490
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000636 0.001200 YES
Predicted change in Energy=-1.036447D-08
Optimization completed.
</pre>

[[image:2br at top IR.svg|650px|center|thumb|Figure 1.Isomer 4 IR]]

Based on the data collected, due to that the atoms are all the same, therefore the four IR spectra show the same 18 vibrational frequencies, which is calculated by the formula '''Vibrational Mod = 3N-6'''. Whenever there is a change in dipole moment, an IR active peak will be generated.

According to four IR spectra diagrams, it can be seen that isomer 2 (Point Group C1)has a largest number of bands in its' IR spectra. The reason is that it is the most non-symmetric conformer. What's more, all the vibrational frequencies are IR active and it can be explained by that all intensity are non-zero value. D2h is considered to be the most symmetric conformer. The other isomers with symmetric element shows some IR inactive peaks with intensity equals to 0.

'''Table. Number of IR active vibrational frequency of each isomer'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1(D2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2(C1 )'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3(C2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4(C2v)'''
|-
| Number of IR active.||8||18||10||15
|}

Number of IR active refers to exact the number of bands would show in the IR spectra. All the vibrational frequency values are different, therefore there are no degenerated energy levels.

===Al-Br stretch analysis===

'''Table. Vibrational frequency Mode 15 Al-Br stretch comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Mode 15.Vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Isomer 1||[[image:2br inmid -15.gif|center|250px|center]]||467.23||346.55||rowspan="2" | By comparing these diagrams, the same mode of vibrational frequency are pre-set. The former one shows vigorous bridged Al-Br stretch with little bent. The later one shows both strong terminal Al-Br stretch and bent.
|-
| Isomer 2||[[image:1br inmid -15.gif|center|250px|center]]||423.93||274.48
|}

'''Table. Isomer 2 Al-Br stretch comparison at different vibrational frequency '''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''type ofVibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| at mode 11||[[image:1 br in mid -11.gif|center|250px|center]]||211.12||20.96||rowspan="2" | These two vibrational frequency moving diagrams are basically got from the same isomer (1 Br at bridged position and 1Br at terminal position). At low vibrational frequency, the Al-Br (bridged positon) bond stretches more vigorously while the Al-Br (terminal) bond only bents left and right. At high vibrational frequency, on the contrary, the Al-Br (terminal) bond tends to stretches more vigorously while the Al-Br (bridged positon) bond only bents up and down. What's more, from the mode 11 diagram, we can see that two bridged Al-Br bonds stretch more vigorously than the two bridged Al-Cl bonds do( or in mode 17 diagram, bridged Al-Br bond (Al adjacent to the terminal Br) bents more vigorously than the other bridged Al-Br bond.
|-
| at mode 17||[[image:1br inmid -17.gif|center|250px|center]]||574.34||121.85
|}

===Molecular Orbital of Al2Cl4Br2===

In the section, the MO Calculation of the lowest energy conformer is carried out, which is isomer 3 with two terminal Br at diagonal position.

<pre>
opt-br-up-down energy
File Name = br up and down energy
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -2352.41631610 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 0.0013 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 31.2 seconds.
</pre>

Full Isomer 3 (lowest energy conformer) energy log file is liked to [[media:Br up and down energy.log| here]].

'''Table. Five MOs ranging from highly antibonding to highly bonding'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Structure'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Highly Antibonding ||[[image:Antibonding -60 -1.PNG|left|200px|center|]] [[image:Antibonding -60 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 60. Generally, all interactions are antibonding. Angular node , non electron density is delocalised. '''Overall strong antibonding interactions'''
|-
| LUMO||[[image:LUMO -1 55.PNG|left|200px|center|]][[image:LUMO -2 55.PNG|left|200px|center|]]||These molecular diagrams are chosen from energy level 55-LUMO. The strong through-bond antibonding interactions between the terminal halides and center Al and the strong through-bond bonding interactions between the bridged haildes and the center Al are cancelled out. Therefore, weak through space bonding interactions dominates. Angular node and radial node, electron density delocalised between the center Al and the bridged halides. '''Overall slightly bonding interactions'''
|-
| HOMO||[[image:HOMO MO-54.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 54-HOMO. The weak through space bonding interactions between the bridged halides and the weak through space bonding interactions between the terminal halides slightly outweigh the weak through space antibonding interactions between the terminal halides and the bridged halides. Angular node, no electron density delocalised. '''Overall slightly bonding interactions'''
|-
| Bonding ||[[image:Antibonding -58.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 58. The strong through-bond bonding interactions between terminal halides and the center Al slightly overwhelm the strong through-bond antibonding interactions acting at the same bonds. There are also weak through space bonding interactions between the terminal haldies. Angular node and radial node, electron density delocalised between the center Al and the terminal and bridged haldies '''Overall bonding interactions'''
|-
| Highly bonding||[[image:Bonding -41 -1- annotate.png|left|200px|center|]][[image:Bonding -41 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 41. Generally, all interactions are bonding. Angular node, electron density delocalised between the terminal halides and the center Al. Electron density also delocalised between the two bridged halides. '''Overall strong bonding interactions'''

|}

NB.An angular node is a flat plane. A radial node is a circular ring.

==Reference==

<references/>

File:Br up and down energy.log

2013-11-22T11:54:20Z

Yz8711:

Rep:Mod:Qsmzhl1

2013-11-22T11:47:08Z

Yz8711: /* Al-Br stretch analysis */

==Computational Chemistry Inorganic module Lab==

===Optimising a Molecule of BH3===

Create a BH3 molecule, set one B-H bond to 1.53 angstrom, one B-H bond to 1.54 angstrom, and the third B-H bond to 1.55 angstrom.

====BH3 3-21G optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
</pre>

Full BH3 3-21G optimisation log file is liked to [[media:Yiyun bh3 opt2.LOG| here]].

'''Table 1. BH3 3-21G Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.94Å||120.00°
|}

'''BH3 3-21G optimisation summary'''
<pre>
BH3 optimisation
File Name = yiyun_bh3_opt2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 3-21G
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.46226429 a.u.
RMS Gradient Norm = 0.00008851 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.
</pre>

[[image:BH3 321g optimisation.PNG|left|700px|center|thumb|Figure 1.total energy curve and RMS gradient]]

 
These two graphs illustrate the process of BH3 3-21G optimisation, while the first shows the energy of the molecule at each step and the second gives the gradient of optimisation of each step of optimisation. When the gradient shows a value which is very close to zero, it means the optimisation is completed.

===Using a better basis set===

====BH3 6-31G(d,p) optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
</pre>

Full BH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN BH3 OPT2 631GDP.LOG| here]].

'''Table 2. BH3 6-31G(d,p) Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.19Å|| 1.196Å<ref name="BH distance">Peng, Bin; Li, Qian-Shu; Xie, Yaoming; Bruce King, R.; Schaefer, Henry F. III
Chemical Physics, 2009 , vol. 356, p. 171 - 176;{{DOI|10.1016/j.chemphys.2008.10.050}}</ref>||120.00°
|}

'''BH3 6-31G(d,p) optimisation summary'''
<pre>
BH3 optimisation 631g
File Name = yiyun_bh3_opt2_631gdp
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532360 a.u.
RMS Gradient Norm = 0.00000707 a.u.
Imaginary Freq =
Dipole Moment = 0.0001 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 41.0 seconds.
</pre>

'''Table 3. Total energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 3-21G'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 6-31G(d,p)'''
|-
| -26.46226429 a.u.||-26.61532360 a.u.
|}

===Using pseudo-potentials and larger basis sets===

====GaBr3 optimisation====

<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
Predicted change in Energy=-1.282692D-12
Optimization completed.
</pre>

Full GaBr3 LanL2DZ optimisation log file is liked to [[media:GaBr3 opt lan.log| here]].

'''GaBr3 LanL2DZ optimisation summary(HPC)'''
<pre>
GaBr3 optimisation
File Name = GaBr3_opt_lan
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000016 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 21.6 seconds.
</pre>

"D-space" link : {{DOI|10042/26121}}

'''Table 4. GaBr3 optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-Ga-Br bond angle'''
|-
| 2.35Å||2.239±0.007Å (at 357K)<ref name="GaBr distance">Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998 , vol. 445, # 1-3 p. 139 - 148; {{DOI|10.1016/S0022-2860(97)00420-1}}</ref>||120.00°
|}

The Gaussian calculated Ga-Br bond distance 2.35 Å is longer than the literature value 2.239±0.007 Å. The gaussian optimised structure is based on gas-phase hypothesis, while the literature value might be figured out through experiment. Therefore, interactions like solid state forces or crystal packing forces will distort the molecule by shrinking the Ga-Br bond distance.

===Using a mixture of basis-sets and psuedo-potentials===

====BBr3 Gen optimisation====

===Reference===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-2.171373D-09
Optimization completed.
</pre>

Full BBr3 Gen optimisation log file is liked to [[media:BBr3 opt.log| here]].

'''BBr3 Gen optimisation summary'''
<pre>
BBr3 optimisation 631g
File Name = BBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43644900 a.u.
RMS Gradient Norm = 0.00000974 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 36.4 seconds.
</pre>

"D-space" link : {{DOI|10042/26129}}

'''Table 5. BBr3 Gen Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-B-Br bond angle'''
|-
| 1.93Å||1.8985Å<ref name="BBr distance">Santiso-Quinnones, Gustavo; Krossing, Ingo Zeitschrift fuer Anorganische und Allgemeine Chemie, 2008 , vol. 634, p. 704 - 707; {{DOI|10.1002/zaac.200700510}}</ref>||120.00°
|}

===Structure Comparison===

====Analysing results====

'''Table. Bond distance comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''BH3'''
| align="center" style="background:#0D4F8B; color: white;"|'''BBr3'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3'''
|-
| Bond distance||1.19Å||1.93Å||2.35Å
|-
| Lit. Bond distance||1.196Å||1.8985Å||2.239Å
|}

By comparing the molecule with same central element and different ligands, take BH3 and BBr3 as an example. The Bond distance is much longer for Boron bond with larger ligand Br compared with Boron bond with H, with 1.196Å and 1.8985Å respectively. The reason to cause such a difference is due to that B-Br has larger electronegativity difference than B-H . Therefore, the polarity bewteen Boron and Br is much strong than the one between Boron and H. This can cause unequal sharing of electrons between atoms, which weaken the bond. (Electronegativity: B=2.04 H=2.20 Br=2.96) Br has an atomic number 17, which is larger compared with H with 1 atomic number. This leads to that Br has a large atomic radius and low positive charge density, therefore poor orbital overlap. The valence shell of Br [[Ar] 4s2 3d10 4p5] is '''p''' orbital, while the valence shell of H is '''s''' orbital.
 
By comparing BBr3 with GaBr3, the bond distance of GaBr3 is slightly larger than BBr3. The same reason to cause such a differece is due to the electronegativity difference for Ga-Br is larger than B-Br, therefore leads to a more unequal sharing of electrons, which weaken the bond.(Electronegativity: B=2.04 Ga=1.81 Br=2.96) Meanwhile, Gallium has a larger atomic number 31[[Ar] 3d10 4s2 4p1], compared with boron with atomic number 5[[He] 2s2 2p1]. Therefore, Gallium has a larger atomic radius and poor positive charge density, leads to the poorer orbital overlap with Br and longer the bond.
 
Yes, the bond does exist! The reason why in some structures don't have any bonds is because that the distance exceeds the pre-defined value set in gaussview. The gaussview draws bonds based on a distance critera!
 
There are three types of bonds, which are covalent bond(formed by sharing electrons), ionic bond(formed by transferring the electrons) and metallic bond(formed by the delocalised electrons gathering at the positive charged metal ion surface).

===Frequency Analysis===

====frequency analysis for BH3====

<pre>
Low frequencies --- -0.9382 -0.8426 -0.0054 5.8717 11.7883 11.8256
Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.909158D-10
Optimization completed.
</pre>

Full BH3 6-31G(d,p) frequency log file is liked to [[media:YIYUN BH3 FREQ.LOG| here]].

'''BH3 6-31G(d,p) frequency summary'''

<pre>
BH3 freq
File Name = YIYUN_BH3_freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = 0.00000284 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 23.0 seconds.
</pre>

====Animating the vibrations====

'''Table'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''form of vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''symmetry D3h point group'''
|-
| 1||[[image:1163.gif|center|250px|center]]Three hydrogen bent in a same direction |||1163||92.55|| A2"
|-
| 2||[[image:1213.gif|center|250px|center]] Two hydrogen bent towards a symmetric direction while the other remains constant||1213.18||14.06|| degenerated E'
|-
| 3||[[image:1213(large).gif|center|250px|center]] Three hydrogen bent towards random directions without any correlation ||1213.19||14.06|| degenerated E'
|-
| 4||[[image:2582.gif|center|250px|center]] Three hydrogen stretch symmetrically||2582.27||0|| totally symmetric A'1
|-
| 5||[[image:2715.gif|center|250px|center]] Two hydrogen stretch in opposite directions against each other (one move towards Boron, the other moves away Boron), the left hydrogen remains constant ||2715.44||126.33|| degenerated E'
|-
| 6||[[image:2715(large).gif|center|250px|center]]Two hydrogen stretch in the same direction against the third hydrogen (two move towards Boron, the other moves away Boron)||2715.45||126.32|| degenerated E'
|}

'''BH3 IR spectrum'''

[[image:BH3 IR spectrum.svg|650px|center|thumb|Figure 1.BH3 IR spectrum]]

From the spectra, it only shows three peaks. However, in the table above, there are six vibration frequencies come out. The reason is that there are two pairs of degenerated energy levels which give the same frequency, with 1213 cm-1 and 2715 cm-1 separately. What's more, the total symmetric energy level A'1 is IR inactive. Therefore, there are only there peaks come out.

===GaBr3 Analysis===

====frequency analysis for GaBr3====

<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
</pre>

Full GaBr3 LanL2DZ frequency log file is liked to [[media:GaBr3freqHPC.log| here]].

'''GaBr3 LanL2DZ frequency summary'''
<pre>
GaBr3 freq
File Name = GaBr3freqHPC
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000011 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 14.2 seconds.
</pre>

"D-space" link : {{DOI|10042/26130}}

'''GaBr3 IR spectrum'''
[[image:GaBr3 IR spectrum.svg|650px|center|thumb|Figure 1.GaBr3 IR spectrum]]

'''Table. BH3 and GaBr3 vibrational frequency comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 Frequency /cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 symmetry D3h point group'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 symmetry D3h point group'''
|-
| 1||1163||92.55||A2"||76.37||3.34||E'
|-
| 2||1213.18||14.06||E'||76.38||3.34||E'
|-
| 3||1213.19||14.06||E'||99.7||9.22||A2"
|-
| 4||2582.27||0||A'1||197.34||0||A1'
|-
| 5||2715.44||126.33||E'||316.18||57.07||E'
|-
| 6||2715.45||126.32||E'||316.19||57.07||E'
|}

Both BH3 and GaBr3 molecule has a D3h point group. That is why they both show six vibration frequencies with two pairs of degenerated e' energy levels, one totally symmetric a1' energy level and one a2" energy level. It also explains why only three peaks shows in IR spectrum. The obvious difference is that GaBr3 has a larger frequency value in general compared with BH3. The reason is that BH bond is more rigid compared with GaBr bond. It is also due to the shorter bond length which refers to larger force constant for BH bond. Therefore, more vibrational energy required to cause a stretch or bent to the structure, result in high vibrational frequency.

Within each molecule, six vibrational frequencies could be allocated into two groups. One is '''bent''' structure and the other is '''stretch''' structure. Take BH3 as an example, according to the MO diagram shown above, frequencies with value 1163-1; 1213.18-1; 1213.19-1 are recognised as '''bent''' structure while the other three left are '''stretch ''' structure. The '''stretch ''' structure shows higher vibrational frequency than '''bent''' structure. The reason might be that changing bond length requires a higher vibrational energy than changing the bond angle does.

It is meaningless to compare the energies with different basis set (or pseudo-potentials) due to that total energy calculation is highly depend on the quality of basis set. The energy difference would be quite large if we using the different basis set to compare, due to that the energy is in unit '''a.u'''. (1 a.u.= 2625kJ/mol)

By carrying out a frequency analysis, we could make sure that we find out the optimised structure with minimal energy through the vibrational frequency and the IR correlated spectrum.

"low frequency" refers to the motions of the center of mass of the molecule. Take BH3 as an example, low frequencies here represent -6 by using the formula '''3N-6 ''', where N is the number of atoms.

===Molecular Orbital of BH3===

'''BH3 energy summary'''
<pre>
BH3 energy
File Name = BH3_631g_energyHPC
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 15.9 seconds.
</pre>
"D-space" link : {{DOI|10042/26135}}

[[image:BH3 MOzyy.gif|left|600px|center|thumb|Figure 2.BH3 molecular orbital diagram]]

'''Table. MO diagrams'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''Energy level'''
| align="center" style="background:#0D4F8B; color: white;"|'''MO diagram'''
|-
| degenerated antibonding 2e'||[[image:2e' 1.JPG|left|150px|center]][[image:2e' 2.JPG|left|150px|center]]
|-
| antibonding 3a1'(LUMO orbital)||[[image:3a1'.JPG|left|150px|center]]
|-
| non-bonding 1a2''||[[image:2a1''.JPG|left|150px|center]]
|-
| degenerated bonding 1e'||[[image:1e' 1.JPG|left|150px|center]][[image:1e' 2.JPG|left|150px|center]]
|-
| bonding 2a1'||[[image:2a1'.JPG|left|150px|center]]
|}

Answer the following questions:

What does this say about the accuracy and usefulness of qualitative MO theory?

Real MOs include the consideration of the electronic density distribution which makes it more diffuse compared with the LCAO MOs as we can see from the diagrams above. The LCAO MOs only shows the clear atomic orbital interactions.

===NBO Analysis===

'''NH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.629718D-09
Optimization completed.
</pre>

Full NH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN NH3 OPT 631G.LOG| here]].

'''NH3 6-31G(d,p) optimisation summary'''
<pre>
NH3 optimisation
File Name = YIYUN_NH3_OPT_631G
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 1 minutes 6.0 seconds.
</pre>

'''NH3 6-31G(d,p) frequency'''
<pre>
Low frequencies --- -7.2856 -7.2001 -7.1997 -0.0020 0.0018 0.0124
Low frequencies --- 1089.2799 1693.9186 1693.9186
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.315803D-10
Optimization completed.
</pre>

Full NH3 6-31G(d,p) frequency log file is liked to [[media:NH3 freq3.log| here]].

'''NH3 6-31G(d,p) frequency summary'''
<pre>
NH3 frequency
File Name = NH3_freq3
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776873 a.u.
RMS Gradient Norm = 0.00000237 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8464 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 22.5 seconds.
</pre>

"D-space" link : {{DOI|10042/26151}}

'''NH3 IR spectrum'''

'''NH3 IR energy summary'''
<pre>
NH3 energy
File Name = NH3_energy
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 32.2 seconds.
</pre>

'''NH3 charge distribution diagrams''
[[image:NH3 charge distribution.PNG|left|200px|center|thumb| charge range:-1.0 to +1.0 ]]

[[image:NH3 charge number.PNG|center|200px|thumb| NBO NH3 with specific charge number]]
 
Red color means highly electronegative, while green color refers to electropositive. The nitrogen has a negative charge of -1.125 and the hydrogen has a positive charge of 0.375.
 

===Association energies: Ammonia-Borane===

'''NH3BH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000024 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.746365D-11
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) optimisation log file is liked to [[media:NH3BH3 OPT 631G 2.LOG| here]].

'''NH3BH3 6-31G(d,p) optimisation summary'''
<pre>
NH3BH3 opt
File Name = NH3BH3_OPT_631G_2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468911 a.u.
RMS Gradient Norm = 0.00000122 a.u.
Imaginary Freq =
Dipole Moment = 5.5647 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

'''NH3BH3 6-31G(d,p) frequency'''

<pre>
Low frequencies --- -5.3030 -0.3083 -0.0451 -0.0011 1.2000 1.2747
Low frequencies --- 263.2955 632.9608 638.4638
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000024 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.117730D-10
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) frequency log file is liked to [[media:NH3BH3 FREQ.LOG| here]].

'''NH3BH3 6-31G(d,p) frequency summary'''

<pre>
NH3BH3 freq
File Name = NH3BH3_FREQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468909 a.u.
RMS Gradient Norm = 0.00000139 a.u.
Imaginary Freq = 0
Dipole Moment = 5.5646 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

'''Table. Frequency energy comparison( Basis set = 6-31G (d,p) )'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(BH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3BH3)'''
|-
| -56.55776873 a.u.||-26.61532363 a.u.||-83.22468909 a.u.
|}

'''Association energy'''
<pre>
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22468909 - [-56.55776873 + (-26.61532363)]
= -0.05159673 a.u.
= -135.47 kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

'''Dissociation energy = 135.47 kJ/mol''' The dissociation energy is positive, therefore it is an endothermic process. It indicates that Ammonia-Borane is more stable.

===Mini Projcet : Lewis acid and base===

===4 possible isomers of Al2Cl4Br2 Optimisation===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Name||2br inmid_opt||1BR INMID_OPT_gen||br up down opt||2br at top_opt
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm||0.00000188||0.00001352||0.00001372||0.00000660
|-
| Imaginary Freq||||||||
|-
| Dipole Moment||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time||0 days 0 hours 7 minutes 23.6 seconds.|| 0 days 0 hours 1 minutes 39.0 seconds.|| 0 days 0 hours 5 minutes 42.7 seconds.||0 days 0 hours 8 minutes 37.5 seconds.
|-
| D-space link || {{DOI|10042/26227}}|| {{DOI|10042/26261}}|| {{DOI|10042/26343}}|| {{DOI|10042/26231}}
|-
| full opt. log file ||[[media:2br inmid opt.log| Isomer 1]] || [[media:1BR INMID OPT gen.LOG| Isomer 2]]||[[media:Br up down opt.log| Isomer 3]] ||[[media:2br at top opt.log| Isomer 4]]
|}

Base on the knowledge we learnt before, the real point group base on the isomer structure shows below:

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Structure||[[image:2br in mid -sym.PNG|left|200px|center|]] ||[[image:1br in mid -sym.PNG|left|200px|center|]] || [[image:Br up and down -sym.PNG|left|200px|center|]]||[[image:2br at top- sym.PNG|left|200px|center|]]
|-
| symmetry elements ||E,C2(z),C2 (y),C2(x,)i,σ(xy),σ(xz),σ(yz)||E||E,C2(z),i,σh||E,C2(z),σv(xz),σv(yz)
|-
| Real point group ||D2h||C1||C2h||C2v
|}

'''Isomer 1 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.944095D-10
Optimization completed.
</pre>

'''Isomer 2 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000548 0.001800 YES
RMS Displacement 0.000196 0.001200 YES
Predicted change in Energy=-2.150173D-08
Optimization completed.
</pre>

'''Isomer 3 optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001062 0.001800 YES
RMS Displacement 0.000483 0.001200 YES
Predicted change in Energy=-1.142040D-08
Optimization completed.
</pre>

'''Isomer 4 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000833 0.001800 YES
RMS Displacement 0.000305 0.001200 YES
Predicted change in Energy=-2.399764D-08
Optimization completed.
</pre>

===AlCl2Br monomer optimisation===

<jmol><jmolApplet><title>Alcl2br freq.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>Alcl2br freq.mol2</uploadedFileContents></jmolApplet></jmol>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984520D-08
Optimization completed.
</pre>

Full AlCl2Br monomer gen optimisation log file is liked to [[media:AlCl2Br opt gen.log| here]].

'''AlCl2Br monomer gen optimisation summary'''

<pre>
AlCl2Br opt
File Name = AlCl2Br opt_gen
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004196 a.u.
Imaginary Freq =
Dipole Moment = 0.1075 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 17.3 seconds.
</pre>

===AlCl2Br monomer frequency analysis===

<pre>
Low frequencies --- 0.0029 0.0030 0.0044 1.3628 3.6408 4.2614
Low frequencies --- 120.5042 133.9180 185.8952
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000082 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000975 0.001200 YES
Predicted change in Energy=-1.813492D-07
Optimization completed.
</pre>

Full AlCl2Br monomer frequency log file is liked to [[media:Alcl2br freq.log| here]].

'''AlCl2Br monomer gen frequency summary'''

<pre>
AlCl2Br freq
File Name = Alcl2br freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004201 a.u.
Imaginary Freq = 0
Dipole Moment = 0.1075 Debye
Point Group = C2V
Job cpu time: 0 days 0 hours 0 minutes 37.4 seconds.
</pre>

[[image:Alcl2br IR.svg|650px|center|thumb|Figure 1.AlCl2Br monomer IR]]

'''Table. Opt Energy comparison of for isomers'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/ a.u.'''
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/kJ/mol'''
| align="center" style="background:#0D4F8B; color: white;"|'''related'''
| align="center" style="background:#0D4F8B; color: white;"|'''Energy difference compared to the lowest one/kJ/mol'''
|-
| Isomer 1||-2352.40630798||-6176240.41||highest||26.28
|-
| Isomer 2||-2352.41109948||-6176252.99||||13.70
|-
| Isomer 3||-2352.41631610||-6176266.69||lowsest||0
|-
| Isomer 4||-2352.41626680||-6176266.56||||0.13
|}

Isomer 3, with two terminal Br at diagonal position, has the lowest energy, indicating the most stable conformer. Isomer 4, with two terminal Br at symmetric position, has the second lowest energy. However, the energy difference is quite small with a value of 0.13kJ/mol only. For those isomers with at least one Br connected at bridged position, by comparing to the most stable conformer(non-Br bridged isomer), it shows a quite large energy gap between them. Isomer 1, with two bridged Br in mid, has the highest energy, indicating the least stable conformer. Isomer 2, with only one Br at bridged position, shows a half value of the difference between the two-Br bridged isomer and non-Br bridged conformer.

The reason to cause such a energy gap can be explained by the difference in overlap between orbitals. Al, Cl and Br have electronic configurations with [[Ne] 3s2 3p1], [[Ne] 3s2 3p5] and [[Ar] 4s2 3d10 4p5] respectively. The 3p-3p (Al-Cl bridged bond)orbital overlap is more stable than 3p-4p(Al-Br bridge bond)orbital overlap, therefore isomer 3 is most stable. Meanwhile, the steric effect would also be a factor to be considered why Cl is more stable at bridged position other than Br.

===Dissociation energy for the lowest energy conformer(Isomer 3)===

'''Opt energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''AlCl2Br'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
|-
| -2352.41631610 a.u.||-1176.19013679 a.u.
|}

<pre>
ΔE= [(E(AlCl2Br)*2)-E(Al2Cl4Br2)]
= [(-1176.19013679*2) - (-2352.41631610)]
= 0.03604252a.u.
= 94.63kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

The dissociation energy computed above is a positive value which indicates it is an endothermic process. Therefore, the product is more favourable than the monomer.

By comparing the monomer with the product dimer, the later one is more stable. It can be explained by that the monomer has only 6 bonded electron in the center Al, which shows a higher electron deficiency than the bridged dimer with 8 electrons in each Al center.

===4 possible isomers of Al2Cl4Br2 Frequency analysis===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FREQ||FREQ||FREQ||FREQ
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)/ a.u.||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm/ a.u.||0.00000188||0.00001354||0.00001368||0.00000657
|-
| Imaginary Freq||||||||
|-
| Dipole Moment/Debye||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time|| 0 days 0 hours 1 minutes 11.9 seconds.|| 0 days 0 hours 3 minutes 31.5 seconds.|| 0 days 0 hours 2 minutes 30.3 seconds.|| 0 days 0 hours 1 minutes 40.9 seconds.
|-
| D-space link||{{DOI|10042/26347}}||{{DOI|10042/26348}}||{{DOI|10042/26349}}||{{DOI|10042/26230}}
|-
| full freq. log file ||[[media:2br inmid freq.log| Isomer 1]] || [[media:1 br in mid freq.log| Isomer 2]]||[[media:Br up down freq.log| Isomer 3]] ||[[media:2br at top freq.log| Isomer 4]]
|}

'''Isomer 1 frequnency'''
<pre>
Low frequencies --- -5.1748 -5.0353 -3.1463 -0.0055 -0.0053 -0.0051
Low frequencies --- 14.8261 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.736206D-10
Optimization completed.
</pre>

[[image:2br inmid IR.svg|650px|center|thumb|Figure 1.Isomer 1 IR]]

'''Isomer 2 frequnency'''
<pre>
Low frequencies --- -2.3182 -0.0011 0.0024 0.0034 1.0656 3.0876
Low frequencies --- 17.1031 55.9263 80.0668
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000887 0.001800 YES
RMS Displacement 0.000381 0.001200 YES
Predicted change in Energy=-3.842255D-08
Optimization completed.
</pre>

[[image:1br in mid IR.svg|650px|center|thumb|Figure 1.Isomer 2 IR]]

'''Isomer 3 frequnency'''
<pre>
Low frequencies --- 0.0034 0.0034 0.0035 1.8920 1.9704 3.9624
Low frequencies --- 18.0988 49.0858 72.9223
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000040 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.001356 0.001800 YES
RMS Displacement 0.000593 0.001200 YES
Predicted change in Energy=-1.805357D-08
Optimization completed.
</pre>

[[image:Up and down IR.svg|650px|center|thumb|Figure 1.Isomer 3 IR]]

'''Isomer 4 frequnency'''
<pre>
Low frequencies --- -4.2528 -2.3928 -0.0052 -0.0050 -0.0043 1.2845
Low frequencies --- 17.1623 50.9093 78.5490
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000636 0.001200 YES
Predicted change in Energy=-1.036447D-08
Optimization completed.
</pre>

[[image:2br at top IR.svg|650px|center|thumb|Figure 1.Isomer 4 IR]]

Based on the data collected, due to that the atoms are all the same, therefore the four IR spectra show the same 18 vibrational frequencies, which is calculated by the formula '''Vibrational Mod = 3N-6'''. Whenever there is a change in dipole moment, an IR active peak will be generated.

According to four IR spectra diagrams, it can be seen that isomer 2 (Point Group C1)has a largest number of bands in its' IR spectra. The reason is that it is the most non-symmetric conformer. What's more, all the vibrational frequencies are IR active and it can be explained by that all intensity are non-zero value. D2h is considered to be the most symmetric conformer. The other isomers with symmetric element shows some IR inactive peaks with intensity equals to 0.

'''Table. Number of IR active vibrational frequency of each isomer'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1(D2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2(C1 )'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3(C2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4(C2v)'''
|-
| Number of IR active.||8||18||10||15
|}

===Molecular Orbital of Al2Cl4Br2===
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Structure'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Highly Antibonding ||[[image:Antibonding -60 -1.PNG|left|200px|center|]] [[image:Antibonding -60 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 60. Generally, all interactions are antibonding. Angular node , non electron density is delocalised. '''Overall strong antibonding interactions'''
|-
| LUMO||[[image:LUMO -1 55.PNG|left|200px|center|]][[image:LUMO -2 55.PNG|left|200px|center|]]||These molecular diagrams are chosen from energy level 55-LUMO. The strong through-bond antibonding interactions between the terminal halides and center Al and the strong through-bond bonding interactions between the bridged haildes and the center Al are cancelled out. Therefore, weak through space bonding interactions dominates. Angular node and radial node, electron density delocalised between the center Al and the bridged halides. '''Overall slightly bonding interactions'''
|-
| HOMO||[[image:HOMO MO-54.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 54-HOMO. The weak through space bonding interactions between the bridged halides and the weak through space bonding interactions between the terminal halides slightly outweigh the weak through space antibonding interactions between the terminal halides and the bridged halides. Angular node, no electron density delocalised. '''Overall slightly bonding interactions'''
|-
| Bonding ||[[image:Antibonding -58.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 58. The strong through-bond bonding interactions between terminal halides and the center Al slightly overwhelm the strong through-bond antibonding interactions acting at the same bonds. There are also weak through space bonding interactions between the terminal haldies. Angular node and radial node, electron density delocalised between the center Al and the terminal and bridged haldies '''Overall bonding interactions'''
|-
| Highly bonding||[[image:Bonding -41 -1- annotate.png|left|200px|center|]][[image:Bonding -41 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 41. Generally, all interactions are bonding. Angular node, electron density delocalised between the terminal halides and the center Al. Electron density also delocalised between the two bridged halides. '''Overall strong bonding interactions'''

|}

NB.An angular node is a flat plane. A radial node is a circular ring.

===Al-Br stretch analysis===

'''Table. Vibrational frequency Mode 15 Al-Br stretch comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Mode 15.Vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Isomer 1||[[image:2br inmid -15.gif|center|250px|center]]||467.23||346.55||rowspan="2" | By comparing these diagrams, the same mode of vibrational frequency are pre-set. The former one shows vigorous bridged Al-Br stretch with little bent. The later one shows both strong terminal Al-Br stretch and bent.
|-
| Isomer 2||[[image:1br inmid -15.gif|center|250px|center]]||423.93||274.48
|}

'''Table. Isomer 2 Al-Br stretch comparison at different vibrational frequency '''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''type ofVibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| at mode 11||[[image:1 br in mid -11.gif|center|250px|center]]||211.12||20.96||rowspan="2" | These two vibrational frequency moving diagrams are basically got from the same isomer (1 Br at bridged position and 1Br at terminal position). At low vibrational frequency, the Al-Br (bridged positon) bond stretches more vigorously while the Al-Br (terminal) bond only bents left and right. At high vibrational frequency, on the contrary, the Al-Br (terminal) bond tends to stretches more vigorously while the Al-Br (bridged positon) bond only bents up and down. What's more, from the mode 11 diagram, we can see that two bridged Al-Br bonds stretch more vigorously than the two bridged Al-Cl bonds do( or in mode 17 diagram, bridged Al-Br bond (Al adjacent to the terminal Br) bents more vigorously than the other bridged Al-Br bond.
|-
| at mode 17||[[image:1br inmid -17.gif|center|250px|center]]||574.34||121.85
|}

==Reference==

<references/>

Rep:Mod:Qsmzhl1

2013-11-22T11:43:49Z

Yz8711: /* Molecular Orbital of Al2Cl4Br2 */

==Computational Chemistry Inorganic module Lab==

===Optimising a Molecule of BH3===

Create a BH3 molecule, set one B-H bond to 1.53 angstrom, one B-H bond to 1.54 angstrom, and the third B-H bond to 1.55 angstrom.

====BH3 3-21G optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
</pre>

Full BH3 3-21G optimisation log file is liked to [[media:Yiyun bh3 opt2.LOG| here]].

'''Table 1. BH3 3-21G Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.94Å||120.00°
|}

'''BH3 3-21G optimisation summary'''
<pre>
BH3 optimisation
File Name = yiyun_bh3_opt2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 3-21G
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.46226429 a.u.
RMS Gradient Norm = 0.00008851 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.
</pre>

[[image:BH3 321g optimisation.PNG|left|700px|center|thumb|Figure 1.total energy curve and RMS gradient]]

 
These two graphs illustrate the process of BH3 3-21G optimisation, while the first shows the energy of the molecule at each step and the second gives the gradient of optimisation of each step of optimisation. When the gradient shows a value which is very close to zero, it means the optimisation is completed.

===Using a better basis set===

====BH3 6-31G(d,p) optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
</pre>

Full BH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN BH3 OPT2 631GDP.LOG| here]].

'''Table 2. BH3 6-31G(d,p) Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.19Å|| 1.196Å<ref name="BH distance">Peng, Bin; Li, Qian-Shu; Xie, Yaoming; Bruce King, R.; Schaefer, Henry F. III
Chemical Physics, 2009 , vol. 356, p. 171 - 176;{{DOI|10.1016/j.chemphys.2008.10.050}}</ref>||120.00°
|}

'''BH3 6-31G(d,p) optimisation summary'''
<pre>
BH3 optimisation 631g
File Name = yiyun_bh3_opt2_631gdp
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532360 a.u.
RMS Gradient Norm = 0.00000707 a.u.
Imaginary Freq =
Dipole Moment = 0.0001 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 41.0 seconds.
</pre>

'''Table 3. Total energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 3-21G'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 6-31G(d,p)'''
|-
| -26.46226429 a.u.||-26.61532360 a.u.
|}

===Using pseudo-potentials and larger basis sets===

====GaBr3 optimisation====

<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
Predicted change in Energy=-1.282692D-12
Optimization completed.
</pre>

Full GaBr3 LanL2DZ optimisation log file is liked to [[media:GaBr3 opt lan.log| here]].

'''GaBr3 LanL2DZ optimisation summary(HPC)'''
<pre>
GaBr3 optimisation
File Name = GaBr3_opt_lan
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000016 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 21.6 seconds.
</pre>

"D-space" link : {{DOI|10042/26121}}

'''Table 4. GaBr3 optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-Ga-Br bond angle'''
|-
| 2.35Å||2.239±0.007Å (at 357K)<ref name="GaBr distance">Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998 , vol. 445, # 1-3 p. 139 - 148; {{DOI|10.1016/S0022-2860(97)00420-1}}</ref>||120.00°
|}

The Gaussian calculated Ga-Br bond distance 2.35 Å is longer than the literature value 2.239±0.007 Å. The gaussian optimised structure is based on gas-phase hypothesis, while the literature value might be figured out through experiment. Therefore, interactions like solid state forces or crystal packing forces will distort the molecule by shrinking the Ga-Br bond distance.

===Using a mixture of basis-sets and psuedo-potentials===

====BBr3 Gen optimisation====

===Reference===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-2.171373D-09
Optimization completed.
</pre>

Full BBr3 Gen optimisation log file is liked to [[media:BBr3 opt.log| here]].

'''BBr3 Gen optimisation summary'''
<pre>
BBr3 optimisation 631g
File Name = BBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43644900 a.u.
RMS Gradient Norm = 0.00000974 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 36.4 seconds.
</pre>

"D-space" link : {{DOI|10042/26129}}

'''Table 5. BBr3 Gen Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-B-Br bond angle'''
|-
| 1.93Å||1.8985Å<ref name="BBr distance">Santiso-Quinnones, Gustavo; Krossing, Ingo Zeitschrift fuer Anorganische und Allgemeine Chemie, 2008 , vol. 634, p. 704 - 707; {{DOI|10.1002/zaac.200700510}}</ref>||120.00°
|}

===Structure Comparison===

====Analysing results====

'''Table. Bond distance comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''BH3'''
| align="center" style="background:#0D4F8B; color: white;"|'''BBr3'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3'''
|-
| Bond distance||1.19Å||1.93Å||2.35Å
|-
| Lit. Bond distance||1.196Å||1.8985Å||2.239Å
|}

By comparing the molecule with same central element and different ligands, take BH3 and BBr3 as an example. The Bond distance is much longer for Boron bond with larger ligand Br compared with Boron bond with H, with 1.196Å and 1.8985Å respectively. The reason to cause such a difference is due to that B-Br has larger electronegativity difference than B-H . Therefore, the polarity bewteen Boron and Br is much strong than the one between Boron and H. This can cause unequal sharing of electrons between atoms, which weaken the bond. (Electronegativity: B=2.04 H=2.20 Br=2.96) Br has an atomic number 17, which is larger compared with H with 1 atomic number. This leads to that Br has a large atomic radius and low positive charge density, therefore poor orbital overlap. The valence shell of Br [[Ar] 4s2 3d10 4p5] is '''p''' orbital, while the valence shell of H is '''s''' orbital.
 
By comparing BBr3 with GaBr3, the bond distance of GaBr3 is slightly larger than BBr3. The same reason to cause such a differece is due to the electronegativity difference for Ga-Br is larger than B-Br, therefore leads to a more unequal sharing of electrons, which weaken the bond.(Electronegativity: B=2.04 Ga=1.81 Br=2.96) Meanwhile, Gallium has a larger atomic number 31[[Ar] 3d10 4s2 4p1], compared with boron with atomic number 5[[He] 2s2 2p1]. Therefore, Gallium has a larger atomic radius and poor positive charge density, leads to the poorer orbital overlap with Br and longer the bond.
 
Yes, the bond does exist! The reason why in some structures don't have any bonds is because that the distance exceeds the pre-defined value set in gaussview. The gaussview draws bonds based on a distance critera!
 
There are three types of bonds, which are covalent bond(formed by sharing electrons), ionic bond(formed by transferring the electrons) and metallic bond(formed by the delocalised electrons gathering at the positive charged metal ion surface).

===Frequency Analysis===

====frequency analysis for BH3====

<pre>
Low frequencies --- -0.9382 -0.8426 -0.0054 5.8717 11.7883 11.8256
Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.909158D-10
Optimization completed.
</pre>

Full BH3 6-31G(d,p) frequency log file is liked to [[media:YIYUN BH3 FREQ.LOG| here]].

'''BH3 6-31G(d,p) frequency summary'''

<pre>
BH3 freq
File Name = YIYUN_BH3_freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = 0.00000284 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 23.0 seconds.
</pre>

====Animating the vibrations====

'''Table'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''form of vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''symmetry D3h point group'''
|-
| 1||[[image:1163.gif|center|250px|center]]Three hydrogen bent in a same direction |||1163||92.55|| A2"
|-
| 2||[[image:1213.gif|center|250px|center]] Two hydrogen bent towards a symmetric direction while the other remains constant||1213.18||14.06|| degenerated E'
|-
| 3||[[image:1213(large).gif|center|250px|center]] Three hydrogen bent towards random directions without any correlation ||1213.19||14.06|| degenerated E'
|-
| 4||[[image:2582.gif|center|250px|center]] Three hydrogen stretch symmetrically||2582.27||0|| totally symmetric A'1
|-
| 5||[[image:2715.gif|center|250px|center]] Two hydrogen stretch in opposite directions against each other (one move towards Boron, the other moves away Boron), the left hydrogen remains constant ||2715.44||126.33|| degenerated E'
|-
| 6||[[image:2715(large).gif|center|250px|center]]Two hydrogen stretch in the same direction against the third hydrogen (two move towards Boron, the other moves away Boron)||2715.45||126.32|| degenerated E'
|}

'''BH3 IR spectrum'''

[[image:BH3 IR spectrum.svg|650px|center|thumb|Figure 1.BH3 IR spectrum]]

From the spectra, it only shows three peaks. However, in the table above, there are six vibration frequencies come out. The reason is that there are two pairs of degenerated energy levels which give the same frequency, with 1213 cm-1 and 2715 cm-1 separately. What's more, the total symmetric energy level A'1 is IR inactive. Therefore, there are only there peaks come out.

===GaBr3 Analysis===

====frequency analysis for GaBr3====

<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
</pre>

Full GaBr3 LanL2DZ frequency log file is liked to [[media:GaBr3freqHPC.log| here]].

'''GaBr3 LanL2DZ frequency summary'''
<pre>
GaBr3 freq
File Name = GaBr3freqHPC
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000011 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 14.2 seconds.
</pre>

"D-space" link : {{DOI|10042/26130}}

'''GaBr3 IR spectrum'''
[[image:GaBr3 IR spectrum.svg|650px|center|thumb|Figure 1.GaBr3 IR spectrum]]

'''Table. BH3 and GaBr3 vibrational frequency comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 Frequency /cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 symmetry D3h point group'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 symmetry D3h point group'''
|-
| 1||1163||92.55||A2"||76.37||3.34||E'
|-
| 2||1213.18||14.06||E'||76.38||3.34||E'
|-
| 3||1213.19||14.06||E'||99.7||9.22||A2"
|-
| 4||2582.27||0||A'1||197.34||0||A1'
|-
| 5||2715.44||126.33||E'||316.18||57.07||E'
|-
| 6||2715.45||126.32||E'||316.19||57.07||E'
|}

Both BH3 and GaBr3 molecule has a D3h point group. That is why they both show six vibration frequencies with two pairs of degenerated e' energy levels, one totally symmetric a1' energy level and one a2" energy level. It also explains why only three peaks shows in IR spectrum. The obvious difference is that GaBr3 has a larger frequency value in general compared with BH3. The reason is that BH bond is more rigid compared with GaBr bond. It is also due to the shorter bond length which refers to larger force constant for BH bond. Therefore, more vibrational energy required to cause a stretch or bent to the structure, result in high vibrational frequency.

Within each molecule, six vibrational frequencies could be allocated into two groups. One is '''bent''' structure and the other is '''stretch''' structure. Take BH3 as an example, according to the MO diagram shown above, frequencies with value 1163-1; 1213.18-1; 1213.19-1 are recognised as '''bent''' structure while the other three left are '''stretch ''' structure. The '''stretch ''' structure shows higher vibrational frequency than '''bent''' structure. The reason might be that changing bond length requires a higher vibrational energy than changing the bond angle does.

It is meaningless to compare the energies with different basis set (or pseudo-potentials) due to that total energy calculation is highly depend on the quality of basis set. The energy difference would be quite large if we using the different basis set to compare, due to that the energy is in unit '''a.u'''. (1 a.u.= 2625kJ/mol)

By carrying out a frequency analysis, we could make sure that we find out the optimised structure with minimal energy through the vibrational frequency and the IR correlated spectrum.

"low frequency" refers to the motions of the center of mass of the molecule. Take BH3 as an example, low frequencies here represent -6 by using the formula '''3N-6 ''', where N is the number of atoms.

===Molecular Orbital of BH3===

'''BH3 energy summary'''
<pre>
BH3 energy
File Name = BH3_631g_energyHPC
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 15.9 seconds.
</pre>
"D-space" link : {{DOI|10042/26135}}

[[image:BH3 MOzyy.gif|left|600px|center|thumb|Figure 2.BH3 molecular orbital diagram]]

'''Table. MO diagrams'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''Energy level'''
| align="center" style="background:#0D4F8B; color: white;"|'''MO diagram'''
|-
| degenerated antibonding 2e'||[[image:2e' 1.JPG|left|150px|center]][[image:2e' 2.JPG|left|150px|center]]
|-
| antibonding 3a1'(LUMO orbital)||[[image:3a1'.JPG|left|150px|center]]
|-
| non-bonding 1a2''||[[image:2a1''.JPG|left|150px|center]]
|-
| degenerated bonding 1e'||[[image:1e' 1.JPG|left|150px|center]][[image:1e' 2.JPG|left|150px|center]]
|-
| bonding 2a1'||[[image:2a1'.JPG|left|150px|center]]
|}

Answer the following questions:

What does this say about the accuracy and usefulness of qualitative MO theory?

Real MOs include the consideration of the electronic density distribution which makes it more diffuse compared with the LCAO MOs as we can see from the diagrams above. The LCAO MOs only shows the clear atomic orbital interactions.

===NBO Analysis===

'''NH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.629718D-09
Optimization completed.
</pre>

Full NH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN NH3 OPT 631G.LOG| here]].

'''NH3 6-31G(d,p) optimisation summary'''
<pre>
NH3 optimisation
File Name = YIYUN_NH3_OPT_631G
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 1 minutes 6.0 seconds.
</pre>

'''NH3 6-31G(d,p) frequency'''
<pre>
Low frequencies --- -7.2856 -7.2001 -7.1997 -0.0020 0.0018 0.0124
Low frequencies --- 1089.2799 1693.9186 1693.9186
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.315803D-10
Optimization completed.
</pre>

Full NH3 6-31G(d,p) frequency log file is liked to [[media:NH3 freq3.log| here]].

'''NH3 6-31G(d,p) frequency summary'''
<pre>
NH3 frequency
File Name = NH3_freq3
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776873 a.u.
RMS Gradient Norm = 0.00000237 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8464 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 22.5 seconds.
</pre>

"D-space" link : {{DOI|10042/26151}}

'''NH3 IR spectrum'''

'''NH3 IR energy summary'''
<pre>
NH3 energy
File Name = NH3_energy
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 32.2 seconds.
</pre>

'''NH3 charge distribution diagrams''
[[image:NH3 charge distribution.PNG|left|200px|center|thumb| charge range:-1.0 to +1.0 ]]

[[image:NH3 charge number.PNG|center|200px|thumb| NBO NH3 with specific charge number]]
 
Red color means highly electronegative, while green color refers to electropositive. The nitrogen has a negative charge of -1.125 and the hydrogen has a positive charge of 0.375.
 

===Association energies: Ammonia-Borane===

'''NH3BH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000024 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.746365D-11
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) optimisation log file is liked to [[media:NH3BH3 OPT 631G 2.LOG| here]].

'''NH3BH3 6-31G(d,p) optimisation summary'''
<pre>
NH3BH3 opt
File Name = NH3BH3_OPT_631G_2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468911 a.u.
RMS Gradient Norm = 0.00000122 a.u.
Imaginary Freq =
Dipole Moment = 5.5647 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

'''NH3BH3 6-31G(d,p) frequency'''

<pre>
Low frequencies --- -5.3030 -0.3083 -0.0451 -0.0011 1.2000 1.2747
Low frequencies --- 263.2955 632.9608 638.4638
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000024 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.117730D-10
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) frequency log file is liked to [[media:NH3BH3 FREQ.LOG| here]].

'''NH3BH3 6-31G(d,p) frequency summary'''

<pre>
NH3BH3 freq
File Name = NH3BH3_FREQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468909 a.u.
RMS Gradient Norm = 0.00000139 a.u.
Imaginary Freq = 0
Dipole Moment = 5.5646 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

'''Table. Frequency energy comparison( Basis set = 6-31G (d,p) )'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(BH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3BH3)'''
|-
| -56.55776873 a.u.||-26.61532363 a.u.||-83.22468909 a.u.
|}

'''Association energy'''
<pre>
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22468909 - [-56.55776873 + (-26.61532363)]
= -0.05159673 a.u.
= -135.47 kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

'''Dissociation energy = 135.47 kJ/mol''' The dissociation energy is positive, therefore it is an endothermic process. It indicates that Ammonia-Borane is more stable.

===Mini Projcet : Lewis acid and base===

===4 possible isomers of Al2Cl4Br2 Optimisation===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Name||2br inmid_opt||1BR INMID_OPT_gen||br up down opt||2br at top_opt
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm||0.00000188||0.00001352||0.00001372||0.00000660
|-
| Imaginary Freq||||||||
|-
| Dipole Moment||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time||0 days 0 hours 7 minutes 23.6 seconds.|| 0 days 0 hours 1 minutes 39.0 seconds.|| 0 days 0 hours 5 minutes 42.7 seconds.||0 days 0 hours 8 minutes 37.5 seconds.
|-
| D-space link || {{DOI|10042/26227}}|| {{DOI|10042/26261}}|| {{DOI|10042/26343}}|| {{DOI|10042/26231}}
|-
| full opt. log file ||[[media:2br inmid opt.log| Isomer 1]] || [[media:1BR INMID OPT gen.LOG| Isomer 2]]||[[media:Br up down opt.log| Isomer 3]] ||[[media:2br at top opt.log| Isomer 4]]
|}

Base on the knowledge we learnt before, the real point group base on the isomer structure shows below:

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Structure||[[image:2br in mid -sym.PNG|left|200px|center|]] ||[[image:1br in mid -sym.PNG|left|200px|center|]] || [[image:Br up and down -sym.PNG|left|200px|center|]]||[[image:2br at top- sym.PNG|left|200px|center|]]
|-
| symmetry elements ||E,C2(z),C2 (y),C2(x,)i,σ(xy),σ(xz),σ(yz)||E||E,C2(z),i,σh||E,C2(z),σv(xz),σv(yz)
|-
| Real point group ||D2h||C1||C2h||C2v
|}

'''Isomer 1 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.944095D-10
Optimization completed.
</pre>

'''Isomer 2 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000548 0.001800 YES
RMS Displacement 0.000196 0.001200 YES
Predicted change in Energy=-2.150173D-08
Optimization completed.
</pre>

'''Isomer 3 optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001062 0.001800 YES
RMS Displacement 0.000483 0.001200 YES
Predicted change in Energy=-1.142040D-08
Optimization completed.
</pre>

'''Isomer 4 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000833 0.001800 YES
RMS Displacement 0.000305 0.001200 YES
Predicted change in Energy=-2.399764D-08
Optimization completed.
</pre>

===AlCl2Br monomer optimisation===

<jmol><jmolApplet><title>Alcl2br freq.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>Alcl2br freq.mol2</uploadedFileContents></jmolApplet></jmol>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984520D-08
Optimization completed.
</pre>

Full AlCl2Br monomer gen optimisation log file is liked to [[media:AlCl2Br opt gen.log| here]].

'''AlCl2Br monomer gen optimisation summary'''

<pre>
AlCl2Br opt
File Name = AlCl2Br opt_gen
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004196 a.u.
Imaginary Freq =
Dipole Moment = 0.1075 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 17.3 seconds.
</pre>

===AlCl2Br monomer frequency analysis===

<pre>
Low frequencies --- 0.0029 0.0030 0.0044 1.3628 3.6408 4.2614
Low frequencies --- 120.5042 133.9180 185.8952
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000082 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000975 0.001200 YES
Predicted change in Energy=-1.813492D-07
Optimization completed.
</pre>

Full AlCl2Br monomer frequency log file is liked to [[media:Alcl2br freq.log| here]].

'''AlCl2Br monomer gen frequency summary'''

<pre>
AlCl2Br freq
File Name = Alcl2br freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004201 a.u.
Imaginary Freq = 0
Dipole Moment = 0.1075 Debye
Point Group = C2V
Job cpu time: 0 days 0 hours 0 minutes 37.4 seconds.
</pre>

[[image:Alcl2br IR.svg|650px|center|thumb|Figure 1.AlCl2Br monomer IR]]

'''Table. Opt Energy comparison of for isomers'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/ a.u.'''
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/kJ/mol'''
| align="center" style="background:#0D4F8B; color: white;"|'''related'''
| align="center" style="background:#0D4F8B; color: white;"|'''Energy difference compared to the lowest one/kJ/mol'''
|-
| Isomer 1||-2352.40630798||-6176240.41||highest||26.28
|-
| Isomer 2||-2352.41109948||-6176252.99||||13.70
|-
| Isomer 3||-2352.41631610||-6176266.69||lowsest||0
|-
| Isomer 4||-2352.41626680||-6176266.56||||0.13
|}

Isomer 3, with two terminal Br at diagonal position, has the lowest energy, indicating the most stable conformer. Isomer 4, with two terminal Br at symmetric position, has the second lowest energy. However, the energy difference is quite small with a value of 0.13kJ/mol only. For those isomers with at least one Br connected at bridged position, by comparing to the most stable conformer(non-Br bridged isomer), it shows a quite large energy gap between them. Isomer 1, with two bridged Br in mid, has the highest energy, indicating the least stable conformer. Isomer 2, with only one Br at bridged position, shows a half value of the difference between the two-Br bridged isomer and non-Br bridged conformer.

The reason to cause such a energy gap can be explained by the difference in overlap between orbitals. Al, Cl and Br have electronic configurations with [[Ne] 3s2 3p1], [[Ne] 3s2 3p5] and [[Ar] 4s2 3d10 4p5] respectively. The 3p-3p (Al-Cl bridged bond)orbital overlap is more stable than 3p-4p(Al-Br bridge bond)orbital overlap, therefore isomer 3 is most stable. Meanwhile, the steric effect would also be a factor to be considered why Cl is more stable at bridged position other than Br.

===Dissociation energy for the lowest energy conformer(Isomer 3)===

'''Opt energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''AlCl2Br'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
|-
| -2352.41631610 a.u.||-1176.19013679 a.u.
|}

<pre>
ΔE= [(E(AlCl2Br)*2)-E(Al2Cl4Br2)]
= [(-1176.19013679*2) - (-2352.41631610)]
= 0.03604252a.u.
= 94.63kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

The dissociation energy computed above is a positive value which indicates it is an endothermic process. Therefore, the product is more favourable than the monomer.

By comparing the monomer with the product dimer, the later one is more stable. It can be explained by that the monomer has only 6 bonded electron in the center Al, which shows a higher electron deficiency than the bridged dimer with 8 electrons in each Al center.

===4 possible isomers of Al2Cl4Br2 Frequency analysis===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FREQ||FREQ||FREQ||FREQ
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)/ a.u.||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm/ a.u.||0.00000188||0.00001354||0.00001368||0.00000657
|-
| Imaginary Freq||||||||
|-
| Dipole Moment/Debye||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time|| 0 days 0 hours 1 minutes 11.9 seconds.|| 0 days 0 hours 3 minutes 31.5 seconds.|| 0 days 0 hours 2 minutes 30.3 seconds.|| 0 days 0 hours 1 minutes 40.9 seconds.
|-
| D-space link||{{DOI|10042/26347}}||{{DOI|10042/26348}}||{{DOI|10042/26349}}||{{DOI|10042/26230}}
|-
| full freq. log file ||[[media:2br inmid freq.log| Isomer 1]] || [[media:1 br in mid freq.log| Isomer 2]]||[[media:Br up down freq.log| Isomer 3]] ||[[media:2br at top freq.log| Isomer 4]]
|}

'''Isomer 1 frequnency'''
<pre>
Low frequencies --- -5.1748 -5.0353 -3.1463 -0.0055 -0.0053 -0.0051
Low frequencies --- 14.8261 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.736206D-10
Optimization completed.
</pre>

[[image:2br inmid IR.svg|650px|center|thumb|Figure 1.Isomer 1 IR]]

'''Isomer 2 frequnency'''
<pre>
Low frequencies --- -2.3182 -0.0011 0.0024 0.0034 1.0656 3.0876
Low frequencies --- 17.1031 55.9263 80.0668
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000887 0.001800 YES
RMS Displacement 0.000381 0.001200 YES
Predicted change in Energy=-3.842255D-08
Optimization completed.
</pre>

[[image:1br in mid IR.svg|650px|center|thumb|Figure 1.Isomer 2 IR]]

'''Isomer 3 frequnency'''
<pre>
Low frequencies --- 0.0034 0.0034 0.0035 1.8920 1.9704 3.9624
Low frequencies --- 18.0988 49.0858 72.9223
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000040 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.001356 0.001800 YES
RMS Displacement 0.000593 0.001200 YES
Predicted change in Energy=-1.805357D-08
Optimization completed.
</pre>

[[image:Up and down IR.svg|650px|center|thumb|Figure 1.Isomer 3 IR]]

'''Isomer 4 frequnency'''
<pre>
Low frequencies --- -4.2528 -2.3928 -0.0052 -0.0050 -0.0043 1.2845
Low frequencies --- 17.1623 50.9093 78.5490
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000636 0.001200 YES
Predicted change in Energy=-1.036447D-08
Optimization completed.
</pre>

[[image:2br at top IR.svg|650px|center|thumb|Figure 1.Isomer 4 IR]]

Based on the data collected, due to that the atoms are all the same, therefore the four IR spectra show the same 18 vibrational frequencies, which is calculated by the formula '''Vibrational Mod = 3N-6'''. Whenever there is a change in dipole moment, an IR active peak will be generated.

According to four IR spectra diagrams, it can be seen that isomer 2 (Point Group C1)has a largest number of bands in its' IR spectra. The reason is that it is the most non-symmetric conformer. What's more, all the vibrational frequencies are IR active and it can be explained by that all intensity are non-zero value. D2h is considered to be the most symmetric conformer. The other isomers with symmetric element shows some IR inactive peaks with intensity equals to 0.

'''Table. Number of IR active vibrational frequency of each isomer'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1(D2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2(C1 )'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3(C2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4(C2v)'''
|-
| Number of IR active.||8||18||10||15
|}

===Molecular Orbital of Al2Cl4Br2===
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Structure'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Highly Antibonding ||[[image:Antibonding -60 -1.PNG|left|200px|center|]] [[image:Antibonding -60 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 60. Generally, all interactions are antibonding. Angular node , non electron density is delocalised. '''Overall strong antibonding interactions'''
|-
| LUMO||[[image:LUMO -1 55.PNG|left|200px|center|]][[image:LUMO -2 55.PNG|left|200px|center|]]||These molecular diagrams are chosen from energy level 55-LUMO. The strong through-bond antibonding interactions between the terminal halides and center Al and the strong through-bond bonding interactions between the bridged haildes and the center Al are cancelled out. Therefore, weak through space bonding interactions dominates. Angular node and radial node, electron density delocalised between the center Al and the bridged halides. '''Overall slightly bonding interactions'''
|-
| HOMO||[[image:HOMO MO-54.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 54-HOMO. The weak through space bonding interactions between the bridged halides and the weak through space bonding interactions between the terminal halides slightly outweigh the weak through space antibonding interactions between the terminal halides and the bridged halides. Angular node, no electron density delocalised. '''Overall slightly bonding interactions'''
|-
| Bonding ||[[image:Antibonding -58.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 58. The strong through-bond bonding interactions between terminal halides and the center Al slightly overwhelm the strong through-bond antibonding interactions acting at the same bonds. There are also weak through space bonding interactions between the terminal haldies. Angular node and radial node, electron density delocalised between the center Al and the terminal and bridged haldies '''Overall bonding interactions'''
|-
| Highly bonding||[[image:Bonding -41 -1- annotate.png|left|200px|center|]][[image:Bonding -41 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 41. Generally, all interactions are bonding. Angular node, electron density delocalised between the terminal halides and the center Al. Electron density also delocalised between the two bridged halides. '''Overall strong bonding interactions'''

|}

NB.An angular node is a flat plane. A radial node is a circular ring.

===Al-Br stretch analysis===

'''Table. Vibrational frequency Mode 15 Al-Br stretch comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Mode 15.Vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Isomer 1||[[image:2br inmid -15.gif|center|250px|center]]||467.23||346.55||rowspan="2" | By comparing these diagrams, the same mode of vibrational frequency are pre-set. The former one shows vigorous bridged Al-Br stretch with little bent. The later one shows both strong terminal Al-Br stretch and bent.
|-
| Isomer 2||[[image:1br inmid -15.gif|center|250px|center]]||423.93||274.48
|}

'''Table. Isomer 2 Al-Br stretch comparison at different vibrational frequency '''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''type ofVibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| at mode 11||[[image:1 br in mid -11.gif|center|250px|center]]||211.12||20.96||rowspan="2" | These two vibrational frequency moving diagrams are basically got from the same isomer(1 Br at bridged position and 1Br at terminal position-Isomer 2). At low vibrational frequency, the Al-Br (bridged positon) bond stretches more vigorously while the Al-Br (terminal) bond only bents left and right. At high vibrational frequency, on the contrary, the Al-Br (terminal) bond tends to stretches more vigorously while the Al-Br (bridged positon) bond only bents up and down. What's more, from the mode 11 diagram, we can see that two bridged Al-Br bonds stretch more vigorously than the two bridged Al-Cl bonds do( or in mode 17 diagram, bridged Al-Br bond (Al adjacent to the terminal Br) bents more vigorously than the other bridged Al-Br bond.
|-
| at mode 17||[[image:1br inmid -17.gif|center|250px|center]]||574.34||121.85
|}

==Reference==

<references/>

Rep:Mod:Qsmzhl1

2013-11-22T11:25:10Z

2013-11-21T21:10:19Z

Yz8711: /* Molecular Orbital of Al2Cl4Br2 */

==Computational Chemistry Inorganic module Lab==

===Optimising a Molecule of BH3===

Create a BH3 molecule, set one B-H bond to 1.53 angstrom, one B-H bond to 1.54 angstrom, and the third B-H bond to 1.55 angstrom.

====BH3 3-21G optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000220 0.000450 YES
RMS Force 0.000106 0.000300 YES
Maximum Displacement 0.000709 0.001800 YES
RMS Displacement 0.000447 0.001200 YES
Predicted change in Energy=-1.672478D-07
Optimization completed.
</pre>

Full BH3 3-21G optimisation log file is liked to [[media:Yiyun bh3 opt2.LOG| here]].

'''Table 1. BH3 3-21G Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.94Å||120.00°
|}

'''BH3 3-21G optimisation summary'''
<pre>
BH3 optimisation
File Name = yiyun_bh3_opt2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 3-21G
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.46226429 a.u.
RMS Gradient Norm = 0.00008851 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 38.0 seconds.
</pre>

[[image:BH3 321g optimisation.PNG|left|700px|center|thumb|Figure 1.total energy curve and RMS gradient]]

 
These two graphs illustrate the process of BH3 3-21G optimisation, while the first shows the energy of the molecule at each step and the second gives the gradient of optimisation of each step of optimisation. When the gradient shows a value which is very close to zero, it means the optimisation is completed.

===Using a better basis set===

====BH3 6-31G(d,p) optimisation====

<pre>
Item Value Threshold Converged?
Maximum Force 0.000012 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.000061 0.001800 YES
RMS Displacement 0.000038 0.001200 YES
Predicted change in Energy=-1.069855D-09
Optimization completed.
</pre>

Full BH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN BH3 OPT2 631GDP.LOG| here]].

'''Table 2. BH3 6-31G(d,p) Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-H bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd H-B-H bond angle'''
|-
| 1.19Å|| 1.196Å<ref name="BH distance">Peng, Bin; Li, Qian-Shu; Xie, Yaoming; Bruce King, R.; Schaefer, Henry F. III
Chemical Physics, 2009 , vol. 356, p. 171 - 176;{{DOI|10.1016/j.chemphys.2008.10.050}}</ref>||120.00°
|}

'''BH3 6-31G(d,p) optimisation summary'''
<pre>
BH3 optimisation 631g
File Name = yiyun_bh3_opt2_631gdp
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532360 a.u.
RMS Gradient Norm = 0.00000707 a.u.
Imaginary Freq =
Dipole Moment = 0.0001 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 41.0 seconds.
</pre>

'''Table 3. Total energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 3-21G'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 6-31G(d,p)'''
|-
| -26.46226429 a.u.||-26.61532360 a.u.
|}

===Using pseudo-potentials and larger basis sets===

====GaBr3 optimisation====

<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
Predicted change in Energy=-1.282692D-12
Optimization completed.
</pre>

Full GaBr3 LanL2DZ optimisation log file is liked to [[media:GaBr3 opt lan.log| here]].

'''GaBr3 LanL2DZ optimisation summary(HPC)'''
<pre>
GaBr3 optimisation
File Name = GaBr3_opt_lan
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000016 a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 21.6 seconds.
</pre>

"D-space" link : {{DOI|10042/26121}}

'''Table 4. GaBr3 optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. Ga-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-Ga-Br bond angle'''
|-
| 2.35Å||2.239±0.007Å (at 357K)<ref name="GaBr distance">Reffy, Balazs; Kolonits, Maria; Hargittai, Magdolna Journal of Molecular Structure, 1998 , vol. 445, # 1-3 p. 139 - 148; {{DOI|10.1016/S0022-2860(97)00420-1}}</ref>||120.00°
|}

The Gaussian calculated Ga-Br bond distance 2.35 Å is longer than the literature value 2.239±0.007 Å. The gaussian optimised structure is based on gas-phase hypothesis, while the literature value might be figured out through experiment. Therefore, interactions like solid state forces or crystal packing forces will distort the molecule by shrinking the Ga-Br bond distance.

===Using a mixture of basis-sets and psuedo-potentials===

====BBr3 Gen optimisation====

===Reference===
<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.000106 0.001800 YES
RMS Displacement 0.000061 0.001200 YES
Predicted change in Energy=-2.171373D-09
Optimization completed.
</pre>

Full BBr3 Gen optimisation log file is liked to [[media:BBr3 opt.log| here]].

'''BBr3 Gen optimisation summary'''
<pre>
BBr3 optimisation 631g
File Name = BBr3_opt
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -64.43644900 a.u.
RMS Gradient Norm = 0.00000974 a.u.
Imaginary Freq =
Dipole Moment = 0.0003 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 0 minutes 36.4 seconds.
</pre>

"D-space" link : {{DOI|10042/26129}}

'''Table 5. BBr3 Gen Optimised bond distance and angle'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''optimised B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''lit. B-Br bond distance'''
| align="center" style="background:#0D4F8B; color: white;"|'''optimisd Br-B-Br bond angle'''
|-
| 1.93Å||1.8985Å<ref name="BBr distance">Santiso-Quinnones, Gustavo; Krossing, Ingo Zeitschrift fuer Anorganische und Allgemeine Chemie, 2008 , vol. 634, p. 704 - 707; {{DOI|10.1002/zaac.200700510}}</ref>||120.00°
|}

===Structure Comparison===

====Analysing results====

'''Table. Bond distance comparison'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''BH3'''
| align="center" style="background:#0D4F8B; color: white;"|'''BBr3'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3'''
|-
| Bond distance||1.19Å||1.93Å||2.35Å
|-
| Lit. Bond distance||1.196Å||1.8985Å||2.239Å
|}

By comparing the molecule with same central element and different ligands, take BH3 and BBr3 as an example. The Bond distance is much longer for Boron bond with larger ligand Br compared with Boron bond with H, with 1.196Å and 1.8985Å respectively. The reason to cause such a difference is due to that B-Br has larger electronegativity difference than B-H . Therefore, the polarity bewteen Boron and Br is much strong than the one between Boron and H. This can cause unequal sharing of electrons between atoms, which weaken the bond. (Electronegativity: B=2.04 H=2.20 Br=2.96) Br has an atomic number 17, which is larger compared with H with 1 atomic number. This leads to that Br has a large atomic radius and low positive charge density, therefore poor orbital overlap. The valence shell of Br [[Ar] 4s2 3d10 4p5] is '''p''' orbital, while the valence shell of H is '''s''' orbital.
 
By comparing BBr3 with GaBr3, the bond distance of GaBr3 is slightly larger than BBr3. The same reason to cause such a differece is due to the electronegativity difference for Ga-Br is larger than B-Br, therefore leads to a more unequal sharing of electrons, which weaken the bond.(Electronegativity: B=2.04 Ga=1.81 Br=2.96) Meanwhile, Gallium has a larger atomic number 31[[Ar] 3d10 4s2 4p1], compared with boron with atomic number 5[[He] 2s2 2p1]. Therefore, Gallium has a larger atomic radius and poor positive charge density, leads to the poorer orbital overlap with Br and longer the bond.
 
Yes, the bond does exist! The reason why in some structures don't have any bonds is because that the distance exceeds the pre-defined value set in gaussview. The gaussview draws bonds based on a distance critera!
 
There are three types of bonds, which are covalent bond(formed by sharing electrons), ionic bond(formed by transferring the electrons) and metallic bond(formed by the delocalised electrons gathering at the positive charged metal ion surface).

===Frequency Analysis===

====frequency analysis for BH3====

<pre>
Low frequencies --- -0.9382 -0.8426 -0.0054 5.8717 11.7883 11.8256
Low frequencies --- 1162.9968 1213.1829 1213.1856
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-1.909158D-10
Optimization completed.
</pre>

Full BH3 6-31G(d,p) frequency log file is liked to [[media:YIYUN BH3 FREQ.LOG| here]].

'''BH3 6-31G(d,p) frequency summary'''

<pre>
BH3 freq
File Name = YIYUN_BH3_freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = 0.00000284 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 23.0 seconds.
</pre>

====Animating the vibrations====

'''Table'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''form of vibration'''
| align="center" style="background:#0D4F8B; color: white;"|'''frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''symmetry D3h point group'''
|-
| 1||[[image:1163.gif|center|250px|center]]Three hydrogen bent in a same direction |||1163||92.55|| A2"
|-
| 2||[[image:1213.gif|center|250px|center]] Two hydrogen bent towards a symmetric direction while the other remains constant||1213.18||14.06|| degenerated E'
|-
| 3||[[image:1213(large).gif|center|250px|center]] Three hydrogen bent towards random directions without any correlation ||1213.19||14.06|| degenerated E'
|-
| 4||[[image:2582.gif|center|250px|center]] Three hydrogen stretch symmetrically||2582.27||0|| totally symmetric A'1
|-
| 5||[[image:2715.gif|center|250px|center]] Two hydrogen stretch in opposite directions against each other (one move towards Boron, the other moves away Boron), the left hydrogen remains constant ||2715.44||126.33|| degenerated E'
|-
| 6||[[image:2715(large).gif|center|250px|center]]Two hydrogen stretch in the same direction against the third hydrogen (two move towards Boron, the other moves away Boron)||2715.45||126.32|| degenerated E'
|}

'''BH3 IR spectrum'''

[[image:BH3 IR spectrum.svg|650px|center|thumb|Figure 1.BH3 IR spectrum]]

From the spectra, it only shows three peaks. However, in the table above, there are six vibration frequencies come out. The reason is that there are two pairs of degenerated energy levels which give the same frequency, with 1213 cm-1 and 2715 cm-1 separately. What's more, the total symmetric energy level A'1 is IR inactive. Therefore, there are only there peaks come out.

===GaBr3 Analysis===

====frequency analysis for GaBr3====

<pre>
Low frequencies --- -0.5252 -0.5247 -0.0024 -0.0010 0.0235 1.2010
Low frequencies --- 76.3744 76.3753 99.6982
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000000 0.000450 YES
RMS Force 0.000000 0.000300 YES
Maximum Displacement 0.000002 0.001800 YES
RMS Displacement 0.000001 0.001200 YES
Predicted change in Energy=-6.142862D-13
Optimization completed.
</pre>

Full GaBr3 LanL2DZ frequency log file is liked to [[media:GaBr3freqHPC.log| here]].

'''GaBr3 LanL2DZ frequency summary'''
<pre>
GaBr3 freq
File Name = GaBr3freqHPC
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = LANL2DZ
Charge = 0
Spin = Singlet
E(RB3LYP) = -41.70082783 a.u.
RMS Gradient Norm = 0.00000011 a.u.
Imaginary Freq = 0
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 14.2 seconds.
</pre>

"D-space" link : {{DOI|10042/26130}}

'''GaBr3 IR spectrum'''
[[image:GaBr3 IR spectrum.svg|650px|center|thumb|Figure 1.GaBr3 IR spectrum]]

'''Table. BH3 and GaBr3 vibrational frequency comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''No.'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 Frequency /cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''BH3 symmetry D3h point group'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 Frequency/cm-1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Intensity'''
| align="center" style="background:#0D4F8B; color: white;"|'''GaBr3 symmetry D3h point group'''
|-
| 1||1163||92.55||A2"||76.37||3.34||E'
|-
| 2||1213.18||14.06||E'||76.38||3.34||E'
|-
| 3||1213.19||14.06||E'||99.7||9.22||A2"
|-
| 4||2582.27||0||A'1||197.34||0||A1'
|-
| 5||2715.44||126.33||E'||316.18||57.07||E'
|-
| 6||2715.45||126.32||E'||316.19||57.07||E'
|}

Both BH3 and GaBr3 molecule has a D3h point group. That is why they both show six vibration frequencies with two pairs of degenerated e' energy levels, one totally symmetric a1' energy level and one a2" energy level. It also explains why only three peaks shows in IR spectrum. The obvious difference is that GaBr3 has a larger frequency value in general compared with BH3. The reason is that BH bond is more rigid compared with GaBr bond. It is also due to the shorter bond length which refers to larger force constant for BH bond. Therefore, more vibrational energy required to cause a stretch or bent to the structure, result in high vibrational frequency.

Within each molecule, six vibrational frequencies could be allocated into two groups. One is '''bent''' structure and the other is '''stretch''' structure. Take BH3 as an example, according to the MO diagram shown above, frequencies with value 1163-1; 1213.18-1; 1213.19-1 are recognised as '''bent''' structure while the other three left are '''stretch ''' structure. The '''stretch ''' structure shows higher vibrational frequency than '''bent''' structure. The reason might be that changing bond length requires a higher vibrational energy than changing the bond angle does.

It is meaningless to compare the energies with different basis set (or pseudo-potentials) due to that total energy calculation is highly depend on the quality of basis set. The energy difference would be quite large if we using the different basis set to compare, due to that the energy is in unit '''a.u'''. (1 a.u.= 2625kJ/mol)

By carrying out a frequency analysis, we could make sure that we find out the optimised structure with minimal energy through the vibrational frequency and the IR correlated spectrum.

"low frequency" refers to the motions of the center of mass of the molecule. Take BH3 as an example, low frequencies here represent -6 by using the formula '''3N-6 ''', where N is the number of atoms.

===Molecular Orbital of BH3===

'''BH3 energy summary'''
<pre>
BH3 energy
File Name = BH3_631g_energyHPC
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -26.61532363 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 0.0000 Debye
Point Group = D3H
Job cpu time: 0 days 0 hours 0 minutes 15.9 seconds.
</pre>
"D-space" link : {{DOI|10042/26135}}

[[image:BH3 MOzyy.gif|left|600px|center|thumb|Figure 2.BH3 molecular orbital diagram]]

'''Table. MO diagrams'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''Energy level'''
| align="center" style="background:#0D4F8B; color: white;"|'''MO diagram'''
|-
| degenerated antibonding 2e'||[[image:2e' 1.JPG|left|150px|center]][[image:2e' 2.JPG|left|150px|center]]
|-
| antibonding 3a1'(LUMO orbital)||[[image:3a1'.JPG|left|150px|center]]
|-
| non-bonding 1a2''||[[image:2a1''.JPG|left|150px|center]]
|-
| degenerated bonding 1e'||[[image:1e' 1.JPG|left|150px|center]][[image:1e' 2.JPG|left|150px|center]]
|-
| bonding 2a1'||[[image:2a1'.JPG|left|150px|center]]
|}

Answer the following questions:

What does this say about the accuracy and usefulness of qualitative MO theory?

Real MOs include the consideration of the electronic density distribution which makes it more diffuse compared with the LCAO MOs as we can see from the diagrams above. The LCAO MOs only shows the clear atomic orbital interactions.

===NBO Analysis===

'''NH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000024 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000079 0.001800 YES
RMS Displacement 0.000053 0.001200 YES
Predicted change in Energy=-1.629718D-09
Optimization completed.
</pre>

Full NH3 6-31G(d,p) optimisation log file is liked to [[media:YIYUN NH3 OPT 631G.LOG| here]].

'''NH3 6-31G(d,p) optimisation summary'''
<pre>
NH3 optimisation
File Name = YIYUN_NH3_OPT_631G
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = 0.00000885 a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 1 minutes 6.0 seconds.
</pre>

'''NH3 6-31G(d,p) frequency'''
<pre>
Low frequencies --- -7.2856 -7.2001 -7.1997 -0.0020 0.0018 0.0124
Low frequencies --- 1089.2799 1693.9186 1693.9186
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000007 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000034 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.315803D-10
Optimization completed.
</pre>

Full NH3 6-31G(d,p) frequency log file is liked to [[media:NH3 freq3.log| here]].

'''NH3 6-31G(d,p) frequency summary'''
<pre>
NH3 frequency
File Name = NH3_freq3
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776873 a.u.
RMS Gradient Norm = 0.00000237 a.u.
Imaginary Freq = 0
Dipole Moment = 1.8464 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 22.5 seconds.
</pre>

"D-space" link : {{DOI|10042/26151}}

'''NH3 IR spectrum'''

'''NH3 IR energy summary'''
<pre>
NH3 energy
File Name = NH3_energy
File Type = .log
Calculation Type = SP
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -56.55776856 a.u.
RMS Gradient Norm = a.u.
Imaginary Freq =
Dipole Moment = 1.8464 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 32.2 seconds.
</pre>

'''NH3 charge distribution diagrams''
[[image:NH3 charge distribution.PNG|left|200px|center|thumb| charge range:-1.0 to +1.0 ]]

[[image:NH3 charge number.PNG|center|200px|thumb| NBO NH3 with specific charge number]]
 
Red color means highly electronegative, while green color refers to electropositive. The nitrogen has a negative charge of -1.125 and the hydrogen has a positive charge of 0.375.
 

===Association energies: Ammonia-Borane===

'''NH3BH3 6-31G(d,p) optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000015 YES
RMS Force 0.000001 0.000010 YES
Maximum Displacement 0.000024 0.000060 YES
RMS Displacement 0.000010 0.000040 YES
Predicted change in Energy=-8.746365D-11
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) optimisation log file is liked to [[media:NH3BH3 OPT 631G 2.LOG| here]].

'''NH3BH3 6-31G(d,p) optimisation summary'''
<pre>
NH3BH3 opt
File Name = NH3BH3_OPT_631G_2
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468911 a.u.
RMS Gradient Norm = 0.00000122 a.u.
Imaginary Freq =
Dipole Moment = 5.5647 Debye
Point Group = C1
Job cpu time: 0 days 0 hours 0 minutes 48.0 seconds.
</pre>

'''NH3BH3 6-31G(d,p) frequency'''

<pre>
Low frequencies --- -5.3030 -0.3083 -0.0451 -0.0011 1.2000 1.2747
Low frequencies --- 263.2955 632.9608 638.4638
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000004 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000024 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.117730D-10
Optimization completed.
</pre>

Full NH3BH3 6-31G(d,p) frequency log file is liked to [[media:NH3BH3 FREQ.LOG| here]].

'''NH3BH3 6-31G(d,p) frequency summary'''

<pre>
NH3BH3 freq
File Name = NH3BH3_FREQ
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = 6-31G(d,p)
Charge = 0
Spin = Singlet
E(RB3LYP) = -83.22468909 a.u.
RMS Gradient Norm = 0.00000139 a.u.
Imaginary Freq = 0
Dipole Moment = 5.5646 Debye
Point Group = C3V
Job cpu time: 0 days 0 hours 0 minutes 16.0 seconds.
</pre>

'''Table. Frequency energy comparison( Basis set = 6-31G (d,p) )'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(BH3)'''
| align="center" style="background:#0D4F8B; color: white;"|'''E(NH3BH3)'''
|-
| -56.55776873 a.u.||-26.61532363 a.u.||-83.22468909 a.u.
|}

'''Association energy'''
<pre>
ΔE=E(NH3BH3)-[E(NH3)+E(BH3)]
= -83.22468909 - [-56.55776873 + (-26.61532363)]
= -0.05159673 a.u.
= -135.47 kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

'''Dissociation energy = 135.47 kJ/mol''' The dissociation energy is positive, therefore it is an endothermic process. It indicates that Ammonia-Borane is more stable.

===Mini Projcet : Lewis acid and base===

===4 possible isomers of Al2Cl4Br2 Optimisation===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Name||2br inmid_opt||1BR INMID_OPT_gen||br up down opt||2br at top_opt
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FOPT||FOPT||FOPT||FOPT
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm||0.00000188||0.00001352||0.00001372||0.00000660
|-
| Imaginary Freq||||||||
|-
| Dipole Moment||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time||0 days 0 hours 7 minutes 23.6 seconds.|| 0 days 0 hours 1 minutes 39.0 seconds.|| 0 days 0 hours 5 minutes 42.7 seconds.||0 days 0 hours 8 minutes 37.5 seconds.
|-
| D-space link || {{DOI|10042/26227}}|| {{DOI|10042/26261}}|| {{DOI|10042/26343}}|| {{DOI|10042/26231}}
|-
| full opt. log file ||[[media:2br inmid opt.log| Isomer 1]] || [[media:1BR INMID OPT gen.LOG| Isomer 2]]||[[media:Br up down opt.log| Isomer 3]] ||[[media:2br at top opt.log| Isomer 4]]
|}

Base on the knowledge we learnt before, the real point group base on the isomer structure shows below:

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|
| align="center" style="background:#f0f0f0;"|'''Isomer 1'''
| align="center" style="background:#f0f0f0;"|'''Isomer 2'''
| align="center" style="background:#f0f0f0;"|'''Isomer 3'''
| align="center" style="background:#f0f0f0;"|'''Isomer 4'''
|-
| Structure||[[image:2br in mid -sym.PNG|left|200px|center|]] ||[[image:1br in mid -sym.PNG|left|200px|center|]] || [[image:Br up and down -sym.PNG|left|200px|center|]]||[[image:2br at top- sym.PNG|left|200px|center|]]
|-
| symmetry elements ||E,C2(z),C2 (y),C2(x,)i,σ(xy),σ(xz),σ(yz)||E||E,C2(z),i,σh||E,C2(z),σv(xz),σv(yz)
|-
| Real point group ||D2h||C1||C2h||C2v
|}

'''Isomer 1 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000003 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000057 0.001800 YES
RMS Displacement 0.000015 0.001200 YES
Predicted change in Energy=-2.944095D-10
Optimization completed.
</pre>

'''Isomer 2 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000027 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000548 0.001800 YES
RMS Displacement 0.000196 0.001200 YES
Predicted change in Energy=-2.150173D-08
Optimization completed.
</pre>

'''Isomer 3 optimisation'''

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000008 0.000300 YES
Maximum Displacement 0.001062 0.001800 YES
RMS Displacement 0.000483 0.001200 YES
Predicted change in Energy=-1.142040D-08
Optimization completed.
</pre>

'''Isomer 4 optimisation'''
<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000012 0.000300 YES
Maximum Displacement 0.000833 0.001800 YES
RMS Displacement 0.000305 0.001200 YES
Predicted change in Energy=-2.399764D-08
Optimization completed.
</pre>

===AlCl2Br monomer optimisation===

<jmol><jmolApplet><title>Alcl2br freq.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>Alcl2br freq.mol2</uploadedFileContents></jmolApplet></jmol>
<pre>
Item Value Threshold Converged?
Maximum Force 0.000136 0.000450 YES
RMS Force 0.000073 0.000300 YES
Maximum Displacement 0.000760 0.001800 YES
RMS Displacement 0.000497 0.001200 YES
Predicted change in Energy=-7.984520D-08
Optimization completed.
</pre>

Full AlCl2Br monomer gen optimisation log file is liked to [[media:AlCl2Br opt gen.log| here]].

'''AlCl2Br monomer gen optimisation summary'''

<pre>
AlCl2Br opt
File Name = AlCl2Br opt_gen
File Type = .log
Calculation Type = FOPT
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004196 a.u.
Imaginary Freq =
Dipole Moment = 0.1075 Debye
Point Group = CS
Job cpu time: 0 days 0 hours 1 minutes 17.3 seconds.
</pre>

===AlCl2Br monomer frequency analysis===

<pre>
Low frequencies --- 0.0029 0.0030 0.0044 1.3628 3.6408 4.2614
Low frequencies --- 120.5042 133.9180 185.8952
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000082 0.000450 YES
RMS Force 0.000042 0.000300 YES
Maximum Displacement 0.001588 0.001800 YES
RMS Displacement 0.000975 0.001200 YES
Predicted change in Energy=-1.813492D-07
Optimization completed.
</pre>

Full AlCl2Br monomer frequency log file is liked to [[media:Alcl2br freq.log| here]].

'''AlCl2Br monomer gen frequency summary'''

<pre>
AlCl2Br freq
File Name = Alcl2br freq
File Type = .log
Calculation Type = FREQ
Calculation Method = RB3LYP
Basis Set = Gen
Charge = 0
Spin = Singlet
E(RB3LYP) = -1176.19013679 a.u.
RMS Gradient Norm = 0.00004201 a.u.
Imaginary Freq = 0
Dipole Moment = 0.1075 Debye
Point Group = C2V
Job cpu time: 0 days 0 hours 0 minutes 37.4 seconds.
</pre>

[[image:Alcl2br IR.svg|650px|center|thumb|Figure 1.AlCl2Br monomer IR]]

'''Table. Opt Energy comparison of for isomers'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/ a.u.'''
| align="center" style="background:#0D4F8B; color: white;"|'''Freq E(RB3LYP)/kJ/mol'''
| align="center" style="background:#0D4F8B; color: white;"|'''related'''
| align="center" style="background:#0D4F8B; color: white;"|'''Energy difference compared to the lowest one/kJ/mol'''
|-
| Isomer 1||-2352.40630798||-6176240.41||highest||26.28
|-
| Isomer 2||-2352.41109948||-6176252.99||||13.70
|-
| Isomer 3||-2352.41631610||-6176266.69||lowsest||0
|-
| Isomer 4||-2352.41626680||-6176266.56||||0.13
|}

Isomer 3, with two terminal Br at diagonal position, has the lowest energy, indicating the most stable conformer. Isomer 4, with two terminal Br at symmetric position, has the second lowest energy. However, the energy difference is quite small with a value of 0.13kJ/mol only. For those isomers with at least one Br connected at bridged position, by comparing to the most stable conformer(non-Br bridged isomer), it shows a quite large energy gap between them. Isomer 1, with two bridged Br in mid, has the highest energy, indicating the least stable conformer. Isomer 2, with only one Br at bridged position, shows a half value of the difference between the two-Br bridged isomer and non-Br bridged conformer.

The reason to cause such a energy gap can be explained by the difference in overlap between orbitals. Al, Cl and Br have electronic configurations with [[Ne] 3s2 3p1], [[Ne] 3s2 3p5] and [[Ar] 4s2 3d10 4p5] respectively. The 3p-3p (Al-Cl bridged bond)orbital overlap is more stable than 3p-4p(Al-Br bridge bond)orbital overlap, therefore isomer 3 is most stable. Meanwhile, the steric effect would also be a factor to be considered why Cl is more stable at bridged position other than Br.

===Dissociation energy for the lowest energy conformer(Isomer 3)===

'''Opt energy comparison'''

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|'''AlCl2Br'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
|-
| -2352.41631610 a.u.||-1176.19013679 a.u.
|}

<pre>
ΔE= [(E(AlCl2Br)*2)-E(Al2Cl4Br2)]
= [(-1176.19013679*2) - (-2352.41631610)]
= 0.03604252a.u.
= 94.63kJ/mol

(1 a.u. ≜ 2625.499 62 kJ/mol)
</pre>

The dissociation energy computed above is a positive value which indicates it is an endothermic process. Therefore, the product is more favourable than the monomer.

By comparing the monomer with the product dimer, the later one is more stable. It can be explained by that the monomer has only 6 bonded electron in the center Al, which shows a higher electron deficiency than the bridged dimer with 8 electrons in each Al center.

===4 possible isomers of Al2Cl4Br2 Frequency analysis===

{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4'''
|-
| Structure||<jmol><jmolApplet><title>2br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>2br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br inmid.mol2</title><color>white</color>
<size>200</size><uploadedFileContents>1br inmid.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>1br top 1 bot</title><color>white</color>
<size>200</size><uploadedFileContents>1br top 1 bot.mol2</uploadedFileContents></jmolApplet></jmol>||<jmol><jmolApplet><title>2br at top</title><color>white</color>
<size>200</size><uploadedFileContents>2br at top.mol2</uploadedFileContents></jmolApplet></jmol>
|-
| File Type||.log||.log||.log||.log
|-
| Calculation type||FREQ||FREQ||FREQ||FREQ
|-
| Calculation Method||RB3LYP||RB3LYP||RB3LYP||RB3LYP
|-
| Basis Set ||Gen||Gen||Gen||Gen
|-
| Charge||0||0||0||0
|-
| Spin||Singlet||Singlet||Singlet||Singlet
|-
| E(RB3LYP)/ a.u.||-2352.40630798||-2352.41109948||-2352.41631610||-2352.41626680
|-
| RMS Gradient Norm/ a.u.||0.00000188||0.00001354||0.00001368||0.00000657
|-
| Imaginary Freq||||||||
|-
| Dipole Moment/Debye||0||0.1390||0.0013||0.1690
|-
| Point Group||D2H||C1||CS||C2V
|-
| Job cpu time|| 0 days 0 hours 1 minutes 11.9 seconds.|| 0 days 0 hours 3 minutes 31.5 seconds.|| 0 days 0 hours 2 minutes 30.3 seconds.|| 0 days 0 hours 1 minutes 40.9 seconds.
|-
| D-space link||{{DOI|10042/26347}}||{{DOI|10042/26348}}||{{DOI|10042/26349}}||{{DOI|10042/26230}}
|-
| full freq. log file ||[[media:2br inmid freq.log| Isomer 1]] || [[media:1 br in mid freq.log| Isomer 2]]||[[media:Br up down freq.log| Isomer 3]] ||[[media:2br at top freq.log| Isomer 4]]
|}

'''Isomer 1 frequnency'''
<pre>
Low frequencies --- -5.1748 -5.0353 -3.1463 -0.0055 -0.0053 -0.0051
Low frequencies --- 14.8261 63.2702 86.0770
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000006 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000066 0.001800 YES
RMS Displacement 0.000021 0.001200 YES
Predicted change in Energy=-3.736206D-10
Optimization completed.
</pre>

[[image:2br inmid IR.svg|650px|center|thumb|Figure 1.Isomer 1 IR]]

'''Isomer 2 frequnency'''
<pre>
Low frequencies --- -2.3182 -0.0011 0.0024 0.0034 1.0656 3.0876
Low frequencies --- 17.1031 55.9263 80.0668
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000035 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.000887 0.001800 YES
RMS Displacement 0.000381 0.001200 YES
Predicted change in Energy=-3.842255D-08
Optimization completed.
</pre>

[[image:1br in mid IR.svg|650px|center|thumb|Figure 1.Isomer 2 IR]]

'''Isomer 3 frequnency'''
<pre>
Low frequencies --- 0.0034 0.0034 0.0035 1.8920 1.9704 3.9624
Low frequencies --- 18.0988 49.0858 72.9223
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000040 0.000450 YES
RMS Force 0.000014 0.000300 YES
Maximum Displacement 0.001356 0.001800 YES
RMS Displacement 0.000593 0.001200 YES
Predicted change in Energy=-1.805357D-08
Optimization completed.
</pre>

[[image:Up and down IR.svg|650px|center|thumb|Figure 1.Isomer 3 IR]]

'''Isomer 4 frequnency'''
<pre>
Low frequencies --- -4.2528 -2.3928 -0.0052 -0.0050 -0.0043 1.2845
Low frequencies --- 17.1623 50.9093 78.5490
</pre>

<pre>
Item Value Threshold Converged?
Maximum Force 0.000018 0.000450 YES
RMS Force 0.000007 0.000300 YES
Maximum Displacement 0.001428 0.001800 YES
RMS Displacement 0.000636 0.001200 YES
Predicted change in Energy=-1.036447D-08
Optimization completed.
</pre>

[[image:2br at top IR.svg|650px|center|thumb|Figure 1.Isomer 4 IR]]

Based on the data collected, due to that the atoms are all the same, therefore the four IR spectra show the same 18 vibrational frequencies, which is calculated by the formula '''Vibrational Mod = 3N-6'''. Whenever there is a change in dipole moment, an IR active peak will be generated.

According to four IR spectra diagrams, it can be seen that isomer 2 (Point Group C1)has a largest number of bands in its' IR spectra. The reason is that it is the most non-symmetric conformer. What's more, all the vibrational frequencies are IR active and it can be explained by that all intensity are non-zero value. D2h is considered to be the most symmetric conformer. The other isomers with symmetric element shows some IR inactive peaks with intensity equals to 0.

'''Table. Number of IR active vibrational frequency of each isomer'''
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 1(D2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 2(C1 )'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 3(C2h)'''
| align="center" style="background:#0D4F8B; color: white;"|'''Isomer 4(C2v)'''
|-
| Number of IR active.||8||18||10||15
|}

===Molecular Orbital of Al2Cl4Br2===
{| class="wikitable" border="1"
| align="center" style="background:#0D4F8B; color: white;"|
| align="center" style="background:#0D4F8B; color: white;"|'''Structure'''
| align="center" style="background:#0D4F8B; color: white;"|'''Analysis'''
|-
| Highly Antibonding ||[[image:Antibonding -60 -1.PNG|left|200px|center|]] [[image:Antibonding -60 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 60. Generally, all interactions are antibonding. '''Overall strong antibonding interactions'''
|-
| Highly Antibonding ||[[image:Antibonding -58.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 58. The strong through antibonding interactions between terminal halides and the center Al slightly overwhelm the strong through bonding interactions acting at the same bonds. '''Overall slightly antibonding interactions'''
|-
| LUMO||[[image:LUMO -1 55.PNG|left|200px|center|]][[image:LUMO -2 55.PNG|left|200px|center|]]||These molecular diagrams are chosen from energy level 55-LUMO. The strong through antibonding interactions between the terminal halides and center Al slightly outweigh the strong through bonding interactions between the bridged haildes and the center Al. '''Overall slightly antibonding '''interactions
|-
| HOMO||[[image:HOMO MO-54.PNG|left|200px|center|]]||This molecular diagram is chosen from energy level 54-HOMO. '''Overall slightly bonding interactions'''
|-
| Highly bonding||[[image:Bonding -41 -1- annotate.png|left|200px|center|]][[image:Bonding -41 -2.PNG|left|200px|center|]]|| These molecular diagrams are chosen from energy level 41. '''Overall strong bonding interactions'''
|}

==Reference==

<references/>