ChemWiki - User contributions [en]

Rep:Mod:PhysicalLS

2012-10-29T12:34:21Z

Ls2510: /* The Cope Rearrangement (tutorial) */

This is '''my''' page.

[[User:Ls2510|Ls2510]] 14:12, 22 October 2012 (BST)

== The Cope Rearrangement (tutorial) ==

[[Image:Cope_rearrangement_mechanism.png|center|Mechanism for the Cope rearrangement]]

'''''Anti Peri-planar Optimisation with HF/3-21G Method/Basis Set'''''

* Energy = -231.69253527 a.u.
* Point Group = Ci

'''''Gauche Optimisation with HF/3-21G Method/Basis Set'''''

* Energy = -231.69166701 a.u.
* Point Group = C2

'''''Optimisation of Ci anti 2 with HF/3-21G Method/Basis Set'''''

* Energy = -231.69253522 a.u. (similar result to the table in Appendix 1)
* Point Group = Ci

'''''Optimisation of Ci anti 2 with B3LYP/6-31* Method/Basis Set'''''

* Energy = -234.61170273 a.u.
* Point group = Ci

The structure hasn't visibly changed from using the HF/3-21G method and basis set, but the energy given is far lower.

'''''Frequency Analysis of 1,5-hexadiene Ci Conformer'''''

* Table of low frequencies shows that there are no negative frequencies - so the optimisation has worked and the structure is at a minimum on the potential energy surface:
<pre>
Low frequencies --- -18.8158 -11.7228 -0.0007 -0.0003 -0.0001 1.7045
Low frequencies --- 72.7089 80.1376 120.0097
</pre>

* Energy sums: (extract from .log file)
<pre>
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822
</pre>

=== Optimizing the "Chair" and "Boat" Transition Structures ===

'''''Optimisation of CH2CHCH2 alyl fragment using HF/3-21G Method/Basis Set'''''

* Item table proving the optimisation worked below:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.235912D-08
Optimization completed.
-- Stationary point found.
</pre>

File:Cope rearrangement mechanism.png

2012-10-29T12:33:42Z

Ls2510:

Rep:Mod:PhysicalLS

2012-10-25T12:10:20Z

Ls2510: /* Optimizing the "Chair" and "Boat" Transition Structures */

This is '''my''' page.

[[User:Ls2510|Ls2510]] 14:12, 22 October 2012 (BST)

== The Cope Rearrangement (tutorial) ==

'''''Anti Peri-planar Optimisation with HF/3-21G Method/Basis Set'''''

* Energy = -231.69253527 a.u.
* Point Group = Ci

'''''Gauche Optimisation with HF/3-21G Method/Basis Set'''''

* Energy = -231.69166701 a.u.
* Point Group = C2

'''''Optimisation of Ci anti 2 with HF/3-21G Method/Basis Set'''''

* Energy = -231.69253522 a.u. (similar result to the table in Appendix 1)
* Point Group = Ci

'''''Optimisation of Ci anti 2 with B3LYP/6-31* Method/Basis Set'''''

* Energy = -234.61170273 a.u.
* Point group = Ci

The structure hasn't visibly changed from using the HF/3-21G method and basis set, but the energy given is far lower.

'''''Frequency Analysis of 1,5-hexadiene Ci Conformer'''''

* Table of low frequencies shows that there are no negative frequencies - so the optimisation has worked and the structure is at a minimum on the potential energy surface:
<pre>
Low frequencies --- -18.8158 -11.7228 -0.0007 -0.0003 -0.0001 1.7045
Low frequencies --- 72.7089 80.1376 120.0097
</pre>

* Energy sums: (extract from .log file)
<pre>
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822
</pre>

=== Optimizing the "Chair" and "Boat" Transition Structures ===

'''''Optimisation of CH2CHCH2 alyl fragment using HF/3-21G Method/Basis Set'''''

* Item table proving the optimisation worked below:
<pre>
Item Value Threshold Converged?
Maximum Force 0.000044 0.000450 YES
RMS Force 0.000018 0.000300 YES
Maximum Displacement 0.000175 0.001800 YES
RMS Displacement 0.000073 0.001200 YES
Predicted change in Energy=-1.235912D-08
Optimization completed.
-- Stationary point found.
</pre>

Rep:Mod:PhysicalLS

2012-10-25T11:55:18Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-25T11:53:44Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-23T14:48:43Z

Ls2510: /* The Cope Rearrangement (tutorial) */

This is '''my''' page.

[[User:Ls2510|Ls2510]] 14:12, 22 October 2012 (BST)

== The Cope Rearrangement (tutorial) ==

'''''Anti Peri-planar starting'''''

* Energy = -231.69253527 a.u.
* Point Group = Ci

'''''Gauche starting'''''

* Energy = -231.69166701 a.u.
* Point Group = C2

'''''Optimisation of Ci anti 2 with HF/3-21G'''''

* Energy = -231.69253522 a.u. (similar result to the table in Appendix 1)
* Point Group = Ci

'''''Optimisation of Ci anti 2 with B3LYP/6-31*'''''

* Energy = -234.61170273 a.u.
* Point group = Ci

The structure hasn't visibly changed from using the HF/3-21G method and basis set, but the energy given is far lower.

'''''Frequency Analysis of 1,5-hexadiene Ci Conformer'''''

* Table of low frequencies shows that there are no negative frequencies - so the optimisation has worked and the structure is at a minimum on the potential energy surface:
<pre>
Low frequencies --- -18.8158 -11.7228 -0.0007 -0.0003 -0.0001 1.7045
Low frequencies --- 72.7089 80.1376 120.0097
</pre>

* Energy sums: (extract from .log file)
<pre>
Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822
</pre>

Rep:Mod:PhysicalLS

2012-10-23T14:48:27Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-23T14:29:42Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-23T14:10:10Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-23T14:00:32Z

Ls2510:

Rep:Mod:PhysicalLS

2012-10-22T14:32:44Z

Ls2510: /* The Cope Rearrangement (tutorial) */

Rep:Mod:PhysicalLS

2012-10-22T14:15:11Z

Ls2510:

Rep:Mod:PhysicalLS

2012-10-22T13:12:10Z

Ls2510: Created page with "This is '''my''' page. ~~~~"

This is '''my''' page.

[[User:Ls2510|Ls2510]] 14:12, 22 October 2012 (BST)

Rep:Mod:InorganicLS

2012-10-19T15:54:26Z

Ls2510: /* References */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons"<ref name="Definition" /> which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3<ref name="MO" /> ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==

<references>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="Definition">Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009</ref>
<ref name="MO">http://www.huntresearchgroup.org.uk/teaching/teaching_comp_lab_year3/Tut_MO_diagram_BH3.pdf</ref>
</references>

Rep:Mod:InorganicLS

2012-10-19T15:53:39Z

Ls2510: /* MO Diagram of BH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons"<ref name="Definition" /> which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3<ref name="MO" /> ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==

<references>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="Definition">Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
</references>

Rep:Mod:InorganicLS

2012-10-19T15:52:59Z

Ls2510: /* References */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons"<ref name="Definition" /> which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==

<references>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="Definition">Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
</references>

Rep:Mod:InorganicLS

2012-10-19T15:52:31Z

Ls2510: /* Comparison of BH3, BBr3 and TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons"<ref name="Definition" /> which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==

<references>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
</references>

Rep:Mod:InorganicLS

2012-10-19T15:51:31Z

Ls2510: /* References */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==

<references>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
<ref name="BondLength">http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf</ref>
</references>

Rep:Mod:InorganicLS

2012-10-19T15:50:03Z

Ls2510: /* Optimisation of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref name="BondLength" />, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:47:49Z

Ls2510: /* Table of vibrational modes of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:47:12Z

Ls2510: /* Table of vibrational modes of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]The 2 Br atoms shown with arrows move in a scissoring motion.||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]The two lower Br atoms move back and forth in the same direction while the 3rd Br atom moves in a larger motion in the opposite direction.||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]|The Br atoms move up and down in a together while the Tl atom does the same|a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]The Br atoms move towards and away from the Tl atom together while the Tl atom does not move.||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom opposite to each other while the Tl atoms moves side to side and the 3rd Br is stationary.||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]The lower 2 Br atoms move towards and away from the Tl atom together while the 3rd Br atom has the same movement but opposite, the Tl atom moves opposite to the motion of the Br atoms.||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:41:30Z

Ls2510: /* Comparison of Frequencies of BH3 & TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both. This is because mode 1 in BH3 ("umbrella" deformation) involves the most movement of the central atom, and given Tl is so much heavier than B then it requires more energy for this vibrational mode.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

* The actual movements in the a'1 and higher energy e' are more pronounced (i.e. the atoms move further), which is why they are higher energy because more energy is needed to make them move.

* The frequency analysis must be carried out on a molecule which has already been optimised, and the same basis set must be used for both calculations because the energy of the molecule from optimisation depends greatly on the quality of the basis set used. A very small difference in energy reported in au is a large difference in kJ/mol.

* The optimisation only confirms that the gradient of the potential energy surface is zero, this could correspond to a maximum ''or'' a minimum, so it needs to be confirmed that the molecule generated is truly a minimum. The frequency analysis takes the second derivative of the potential energy surface, so if it is positive we have a minimum and if it is negative we have a maximum.

* Molecules have 3N - 6 vibrations, the low frequencies are simply the "-6", i.e. the motions of the center of mass of the molecule.

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:20:33Z

Ls2510: /* Comparison of Frequencies of BH3 & TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||a'1
|-
| 5||2715||211||e'||e'
|-
| 6||2715||211||e'||e'
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

•What is the purpose of carrying out a frequency analysis?

•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:19:16Z

Ls2510: /* Table of vibrational modes of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||e'
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||a<nowiki>''</nowiki>2
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||
|-
| 5||2715||211||e'||
|-
| 6||2715||211||e'||
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

•What is the purpose of carrying out a frequency analysis?

•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:18:39Z

Ls2510: /* Comparison of Frequencies of BH3 & TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry BH3 (point group D3h)'''
| align="center" style="background:#f0f0f0;"|'''Symmetry TlBr3 (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2||e'
|-
| 2||1213||46||e'||e'
|-
| 3||1213||52||e'||a<nowiki>''</nowiki>2
|-
| 4||2582||156||a'1||
|-
| 5||2715||211||e'||
|-
| 6||2715||211||e'||
|}

* The frequencies of TlBr3 are much lower than BH3, given that wavenumber is proportional to energy, then the Tl-Br bonds are weaker than B-H ones (in agreement with the data of bond lengths earlier). Also both Br and Tl are heavier than H and B respectively so it takes more energy to make the atoms move.

* There has been a re-ordering of modes, what was mode 1 in BH3 is 3 in TlBr3, 2 is changed to 1, 3 is changed to 2, 4 5 and 6 are the same in both.

* The spectra are similar in that the general "shape" of the graph is the same, at low frequencies the a<nowiki>''</nowiki>2 and the e' are together and at high frequencies the a'1 and other e' modes are together.

•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?

•What is the purpose of carrying out a frequency analysis?

•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T15:03:35Z

Ls2510: /* Vibrational Analysis */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

=== Comparison of Frequencies of BH3 & TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''BH3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''TlBr3 Frequency'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||46||a<nowiki>''</nowiki>2
|-
| 2||1213||46||||e'
|-
| 3||1213||52||||e'
|-
| 4||2582||156||a'1
|-
| 5||2715||211||e'
|-
| 6||2715||211||e'
|}

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:54:58Z

Ls2510: /* Vibrational Analysis of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>
* The lowest "real" normal mode is 46.4289 cm-1

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:51:29Z

Ls2510: /* Vibrational Analysis of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to files on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:50:22Z

Ls2510: /* Table of vibrational modes of BH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]] The H atoms move up and down in a together while the B atom does the same but in the opposite direction.||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]] The 2 H atoms shown with arrows move in a scissoring motion.||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]] The two lower H atoms move back and forth in the same direction while the 3rd H atom moves in a larger motion in the opposite direction.||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]] The H atoms move towards and away from the B atom together while the B atom does not move.||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]] The lower 2 H atoms move towards and away from the B atom opposite to each other while the B atoms moves side to side and the 3rd H is stationary.||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]] The lower 2 H atoms move towards and away from the B atom together while the 3rd H atom has the same movement but opposite, the B atom moves opposite to the motion of the H atoms.||e'||
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:36:52Z

Ls2510: /* Comparison of BH3, BBr3 and TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

When GaussView does not draw a bond that does not mean there is no bond, the program has an arbitrary distance for deciding if there is a bond or not and this can be exceeded while there is still ''actually'' a bond present. The bonds in inorganic molecules tend to be longer than those in organic molecules too, so it is more likely for this to be the case in the molecules being analyzed in this exercise.

In reality, there is no hard and fast definition of a bond and it's not so much a binary option of there being a bond or not, but a spectrum of strong bonds to weak interactions. The definition of a bond is "a mutual attraction between two atoms resulting from a redistribution of their outer electrons" REFERENCE which is a very broad definition so it cannot be decided if there is a bond or not just from whether the atoms are within an arbitrary distance of each other.

Collins English Dictionary - Complete & Unabridged 10th Edition
2009 © William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:26:27Z

Ls2510: /* Comparison of BH3, BBr3 and TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''Bond Distance (Angstroms)'''
|-
| BH3||1.19
|-
| BBr3||1.93
|-
| TlBr3||2.65
|}

(All results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set)

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:23:06Z

Ls2510: /* Comparison of BH3, BBr3 and TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

*H-B bond length = 1.19 A (results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set).
*Br-B bond length = 1.93 A
*Br-Tl bond length = 2.65 A

The Br-B bond is longer than H-B, given Br is very electronegative and H is not this can be justified by the Br-B bond being more ionic in character due to bromine withdrawing a large amount of electron density from the boron, i.e. closer to B3+ 3Br- than BBr3

The Br-Tl bonds are much longer again, this could be explained by thallium being very large (81 electrons) and therefore having much more diffuse bonding orbitals than boron, with the electrons less tightly attached to the nucleus so they are easier for bromine to attract and make the bond more ionic (less electrons shared leading to a weaker - hence longer - bond). Also because the atoms Br and Tl are much larger than H and B then the bond will have to be longer simply to accommodate the increased atom size.

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:12:51Z

Ls2510: /* Optimisation */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Comparison of BH3, BBr3 and TlBr3 ===

*H-B bond length = 1.19 A (results from using 6-21G(d,p) basis set. When comparing molecules the calculations have to have been carried out with the same method/basis set).
*B-Br bond length = 1.93 A
*Br-Tl bond length = 2.65 A

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:02:04Z

Ls2510: /* 3-21G Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.4622634 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T14:01:31Z

Ls2510: /* 6-31G(d,p) Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees, Energy = -26.6153237 au

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:28:48Z

Ls2510: /* Ionic Liquids: Designer Solvents (Mini Project) */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

* Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

* Also, the "item" tables proving the molecule has been optimised to a gradient of zero no longer include the summary of optimised parameters, because there are so many atoms in the molecule so the tables are incredibly long.

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:25:13Z

Ls2510: /* Optimisation of NH3BH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,7) 1.0185 -DE/DX = 0.0 !
! R2 R(2,7) 1.0185 -DE/DX = 0.0 !
! R3 R(3,7) 1.0185 -DE/DX = 0.0 !
! R4 R(4,8) 1.2097 -DE/DX = 0.0 !
! R5 R(5,8) 1.2097 -DE/DX = 0.0 !
! R6 R(6,8) 1.2097 -DE/DX = 0.0 !
! R7 R(7,8) 1.6686 -DE/DX = -0.0001 !
! A1 A(1,7,2) 107.8652 -DE/DX = 0.0 !
! A2 A(1,7,3) 107.8652 -DE/DX = 0.0 !
! A3 A(1,7,8) 111.0277 -DE/DX = 0.0 !
! A4 A(2,7,3) 107.8615 -DE/DX = 0.0 !
! A5 A(2,7,8) 111.0375 -DE/DX = 0.0 !
! A6 A(3,7,8) 111.0375 -DE/DX = 0.0 !
! A7 A(4,8,5) 113.9056 -DE/DX = 0.0 !
! A8 A(4,8,6) 113.9056 -DE/DX = 0.0 !
! A9 A(4,8,7) 104.5646 -DE/DX = 0.0001 !
! A10 A(5,8,6) 113.8997 -DE/DX = 0.0 !
! A11 A(5,8,7) 104.5579 -DE/DX = 0.0001 !
! A12 A(6,8,7) 104.5579 -DE/DX = 0.0001 !
! D1 D(1,7,8,4) 180.0 -DE/DX = 0.0 !
! D2 D(1,7,8,5) -59.9968 -DE/DX = 0.0 !
! D3 D(1,7,8,6) 59.9967 -DE/DX = 0.0 !
! D4 D(2,7,8,4) -60.0006 -DE/DX = 0.0 !
! D5 D(2,7,8,5) 60.0026 -DE/DX = 0.0 !
! D6 D(2,7,8,6) 179.9961 -DE/DX = 0.0 !
! D7 D(3,7,8,4) 60.0006 -DE/DX = 0.0 !
! D8 D(3,7,8,5) -179.9962 -DE/DX = 0.0 !
! D9 D(3,7,8,6) -60.0026 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:24:30Z

Ls2510: /* Optimisation of NH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.018 -DE/DX = 0.0 !
! R2 R(1,3) 1.018 -DE/DX = 0.0 !
! R3 R(1,4) 1.018 -DE/DX = 0.0 !
! A1 A(2,1,3) 105.7413 -DE/DX = 0.0 !
! A2 A(2,1,4) 105.7486 -DE/DX = 0.0 !
! A3 A(3,1,4) 105.7479 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -111.8631 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:23:32Z

Ls2510: /* Optimisation of BBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.934 -DE/DX = 0.0 !
! R2 R(1,3) 1.9339 -DE/DX = 0.0 !
! R3 R(1,4) 1.934 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0022 -DE/DX = 0.0 !
! A2 A(2,1,4) 119.9956 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0022 -DE/DX = 0.0 !
! D1 D(2,1,4,3) -180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:22:54Z

Ls2510: /* Optimisation of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 2.651 -DE/DX = 0.0 !
! R2 R(1,3) 2.651 -DE/DX = 0.0 !
! R3 R(1,4) 2.651 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:21:42Z

Ls2510: /* 6-31G(d,p) Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1923 -DE/DX = 0.0 !
! R2 R(1,3) 1.1923 -DE/DX = 0.0 !
! R3 R(1,4) 1.1923 -DE/DX = 0.0 !
! A1 A(2,1,3) 120.0002 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0002 -DE/DX = 0.0 !
! A3 A(3,1,4) 119.9997 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:20:51Z

Ls2510: /* 3-21G Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
----------------------------
! Optimized Parameters !
! (Angstroms and Degrees) !
-------------------------- --------------------------
! Name Definition Value Derivative Info. !
--------------------------------------------------------------------------------
! R1 R(1,2) 1.1935 -DE/DX = 0.0004 !
! R2 R(1,3) 1.1935 -DE/DX = 0.0004 !
! R3 R(1,4) 1.1935 -DE/DX = 0.0004 !
! A1 A(2,1,3) 120.0 -DE/DX = 0.0 !
! A2 A(2,1,4) 120.0 -DE/DX = 0.0 !
! A3 A(3,1,4) 120.0 -DE/DX = 0.0 !
! D1 D(2,1,4,3) 180.0 -DE/DX = 0.0 !
--------------------------------------------------------------------------------
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:16:04Z

Ls2510: /* Energy Comparison */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol. (although the program has an accuracy of +/- 10 kJ/mol so it would be more accurate to report the energy as -140 kJ/mol)

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:12:14Z

Ls2510: /* Optimisation of NH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.02 A, H-N-H bond angle = 105.7 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:11:22Z

Ls2510: /* Table of vibrational modes of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||211||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||211||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:10:45Z

Ls2510: /* Table of vibrational modes of BH3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46.43||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46.43||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52.14||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156.27||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||210.69||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||210.69||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:10:10Z

Ls2510: /* Optimisation of BBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93 A, Br-B-Br bond angles = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162.98||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213.18||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213.24||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582.26||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715.41||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715.44||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46.43||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46.43||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52.14||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156.27||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||210.69||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||210.69||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:09:40Z

Ls2510: /* Optimisation of TlBr3 */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93397 A, Br-B-Br bond angles = 2 x 120.002 & 119.996

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162.98||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213.18||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213.24||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582.26||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715.41||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715.44||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46.43||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46.43||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52.14||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156.27||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||210.69||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||210.69||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:09:17Z

Ls2510: /* 6-31G(d,p) Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65095 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93397 A, Br-B-Br bond angles = 2 x 120.002 & 119.996

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162.98||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213.18||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213.24||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582.26||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715.41||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715.44||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46.43||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46.43||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52.14||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156.27||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||210.69||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||210.69||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1

Rep:Mod:InorganicLS

2012-10-19T13:08:54Z

Ls2510: /* 3-21G Basis Set */

This is '''my''' page.

--[[User:Ls2510|Ls2510]] 14:27, 8 October 2012 (BST)

== Optimisation ==

=== Optimisation of BH3 ===

==== 3-21G Basis Set ====

.log file for this calculation [[Media:BH3_OPT_LS.LOG|here]]

<jmolFile text="BH3 molecule optimized with 3-21G basis set">Bh3_opt_LS.mol‎</jmolFile>

H-B bond length = 1.19 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimized with 3-21G basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||bh3_opt_LS
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||3-21G
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.46226338 a.u.
|-
| RMS Gradient Norm||0.00020672 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job Time||11 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000413 0.000450 YES
RMS Force 0.000271 0.000300 YES
Maximum Displacement 0.001610 0.001800 YES
RMS Displacement 0.001054 0.001200 YES
Predicted change in Energy=-1.071764D-06
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_LS.jpg|350px|Energy optimization graph for BH3]] [[image:Bh3_opt_energygrad_LS.jpg‎|250px|Energy gradient at each step of the optimization]]

==== 6-31G(d,p) Basis Set ====

.log file for this calculation [[Media:GH3_OPT_631GDP_LS.LOG|here]]

‎<jmolFile text="BH3 molecule optimized with 6-31G(d,p) basis set">Bh3_opt_631gdp_LS.mol‎</jmolFile>

H-B bond length = 1.19232 A, H-B-H bond angle = 120 degrees

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 optimization with 6-31G (d,p) basis set'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||GH3_OPT_631GDP
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000236 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||CS
|-
| Job time||49 Seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000012 0.001200 YES
Predicted change in Energy=-1.312911D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bh3_opt_energy_631gdp_LS.jpg|400px|Energy optimization graph for BH3(6-31G basis set)]] [[image:Bh3_opt_energygrad_631gdp_LS.jpg‎|340px|Energy gradient at each step of the optimization(6-31G basis set)]]

=== Optimisation of TlBr3 ===

http://actachemscand.dk/pdf/acta_vol_36a_p0125-0135.pdf lit source, value is 2.512 A

Link to files on D space: {{DOI|10042/20567}}

<jmolFile text="TlBr3 molecule optimized with LanL3DZ basis set">TlBr3_opt_LanL2DZ_LS.mol‎</jmolFile>

Br-Tl bond length = 2.65095 A, Br-Tl-Br bond angle = 120 degrees

The bond length from a literature source is 2.512 A<ref>1</ref>, which is close to the value given by Gaussian (only ~5% difference in value).

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||TlBr3_opt_LanL2DZ
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21750131 a.u.
|-
| RMS Gradient Norm||0.00275003 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0 Debye
|-
| Point Group||D3H
|-
| Job cpu time||21.3 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000014 0.001200 YES
Predicted change in Energy=-6.084037D-11
Optimization completed.
-- Stationary point found.
</pre>

[[image:TlBr3_opt_energy_LanL2DZ_LS.jpg|370px|Energy optimization graph for TlBr3]] [[image:TlBr3_opt_energygrad_LanL2DZ_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

=== Optimisation of BBr3 ===

.log file for this calculation [[Media:BBR3_OPT_GEN_LS.LOG|here]]

<jmolFile text="BBr3 molecule optimized with mixed 6-31G(d,p) basis set and LanL2DZ pseudo-potential">BBR3_OPT_GEN_LS.mol‎</jmolFile>

B-Br bond length = 1.93397 A, Br-B-Br bond angles = 2 x 120.002 & 119.996

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BBr3 optimisation'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||BBR3_OPT_GEN
|-
| File Type||.log
|-
| Calculation Type||FOPT
|-
| Calculation Method||RB3LYP
|-
| Basis Set||Gen
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-64.43645277 a.u.
|-
| RMS Gradient Norm||0.00000384 a.u.
|-
| Imaginary Freq||
|-
| Dipole Moment||0.0002 Debye
|-
| Point Group||CS
|-
| Job cpu time||49.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000008 0.000450 YES
RMS Force 0.000005 0.000300 YES
Maximum Displacement 0.000036 0.001800 YES
RMS Displacement 0.000024 0.001200 YES
Predicted change in Energy=-4.098477D-10
Optimization completed.
-- Stationary point found.
</pre>

[[image:Bbr3_opt_energy_gen_LS.jpg|370px|Energy optimization graph for BBr3]] [[image:Bbr3_opt_energygrad_gen_LS.jpg‎|340px|Energy gradient at each step of the optimization]]

== Vibrational Analysis==

=== Vibrational Analysis of BH3 ===

.log file for this calculation [[Media:LS_BH3_FREQ.LOG‎|here]]

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''BH3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_bh3_freq
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||6-31G(d,p)
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-26.61532374 a.u.
|-
| RMS Gradient Norm||0.00000237 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0 Debye
|-
| Point Group||C2V
|-
| Job cpu time||27.0 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000020 0.001800 YES
RMS Displacement 0.000009 0.001200 YES
Predicted change in Energy=-1.329322D-10
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -18.6669 -0.0009 -0.0003 0.0006 12.5167 12.5631
Low frequencies --- 1162.9785 1213.1756 1213.2363
</pre>

==== Table of vibrational modes of BH3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency (cm-1)'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||1162.98||92.5514||[[Image:LS_BH3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||1213.18||14.0572||[[Image:LS_BH3_VIB2.jpg|200px]]||e'||
|-
| 3||1213.24||14.0608||[[Image:LS_BH3_VIB3.jpg|200px]]||e'||
|-
| 4||2582.26||0||[[Image:LS_BH3_VIB4.jpg|200px]]||a'1||
|-
| 5||2715.41||126.3284||[[Image:LS_BH3_VIB5.jpg|200px]]||e'||
|-
| 6||2715.44||125.3236||[[Image:LS_BH3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR spectrum of BH3 ====

[[Image:LS_BH3_IR.png|center|1000px|IR spectrum of BH3]]

There are 6 vibrations as shown above, yet only 3 peaks in the IR spectrum. This is because the peaks corresponding to the vibrational modes 2 and 3 are incredibly close in frequency and intensity (difference of 0.06 cm-1) so the peaks are superimposed into one peak on the spectrum. This is also the case with modes 5 and 6, which only have a difference in frequency of 0.03 cm-1. (given that the calculations have a systematic error of ~10% the small differences in values are so small as to be meaningless)

This explains 2 of the missing peaks, and the last missing peak is that which would correspond to vibration 4, which has an intensity of 0 and hence no peak.

=== Vibrational Analysis of TlBr3 ===

Link to file on D space: {{DOI|10042/20646}}

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''TlBr3 frequency'''
| align="center" style="background:#f0f0f0;"|''''''
|-
| File Name||LS_TLBR3_FREQ
|-
| File Type||.log
|-
| Calculation Type||FREQ
|-
| Calculation Method||RB3LYP
|-
| Basis Set||LANL2DZ
|-
| Charge||0
|-
| Spin||Singlet
|-
| E(RB3LYP)||-91.21812851 a.u.
|-
| RMS Gradient Norm||0.00000088 a.u.
|-
| Imaginary Freq||0
|-
| Dipole Moment||0
|-
| Point Group||D3H
|-
| Job cpu time||15.9 seconds
|-
|
|}

<pre>
Item Value Threshold Converged?
Maximum Force 0.000002 0.000450 YES
RMS Force 0.000001 0.000300 YES
Maximum Displacement 0.000022 0.001800 YES
RMS Displacement 0.000011 0.001200 YES
Predicted change in Energy=-5.660901D-11
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -3.4213 -0.0026 -0.0004 0.0015 3.9367 3.9367
Low frequencies --- 46.4289 46.4292 52.1449
</pre>

==== Table of vibrational modes of TlBr3 ====

{| class="wikitable" border="1"
| align="center" style="background:#f0f0f0;"|'''Vibrational Mode'''
| align="center" style="background:#f0f0f0;"|'''Frequency'''
| align="center" style="background:#f0f0f0;"|'''Infrared intensity'''
| align="center" style="background:#f0f0f0;"|'''Description of vibration'''
| align="center" style="background:#f0f0f0;"|'''Symmetry (point group D3h)'''
|-
| 1||46.43||3.6867||[[Image:LS_TLBR3_VIB1.jpg|200px]]||a<nowiki>''</nowiki>2||
|-
| 2||46.43||3.6867||[[Image:LS_TLBR3_VIB2.jpg|200px]]||e'||
|-
| 3||52.14||5.8466||[[Image:LS_TLBR3_VIB3.jpg|200px]]||e'||
|-
| 4||156.27||0||[[Image:LS_TLBR3_VIB4.jpg|200px]]||a'1||
|-
| 5||210.69||25.483||[[Image:LS_TLBR3_VIB5.jpg|200px]]||e'||
|-
| 6||210.69||25.4797||[[Image:LS_TLBR3_VIB6.jpg|200px]]||e'||
|-
|
|}

==== IR Spectrum of TlBr3 ====

[[Image:LS_TLBR3_IR.png|center|1000px|IR spectrum of TlBr3]]

now compare and contrast the frequencies for BH3, and TlBr3 on your wiki. (this analysis should be 2-3 paragraphs long.) Some leading questions you should consider are: •What does the large difference in the value of the frequencies for BH3 compared to TlBr3 indicate?
•Has there been a reordering of modes?
•How are these spectra similar?
•For both spectra two modes lie fairly closely together, the A2 and E' modes and then the other two modes also lie fairly close together, the A1' and E' modes, but higher in energy. Why is this?

answer ALL the following in your wiki
•Why must you use the same method and basis set for both the optimisation and frequency analysis calculations?
•What is the purpose of carrying out a frequency analysis?
•What do the "Low frequencies" represent?

== Molecular Orbitals ==

=== Molecular Orbitals of BH3 ===

Link to files on D space: {{DOI|10042/20706}}

==== MO Diagram of BH3 ====

[[Image:BH3_MO_LS.png|1000px|center]]

MO's are shown up to the LUMO, which is a non-bonding orbital. Both the estimate of the MO from LCAO and the MO calculated by Gaussian are displayed. It is apparent from looking at the diagram that the LCAO approximations of MOs are in fact very close to what they "really" are. (Of course the MOs calculated by Gaussian are not exactly correct because a better basis set could be used for example). Therefore qualitative MO theory is accurate and useful, at least for molecules of a similarly small size.

== Natural Bond Orbital Analysis ==

=== NH3 ===

==== Optimisation of NH3 ====

Because NH3 is such a simple molecule, it can be optimised with the 6-21G(d,p) basis set straight away, there is no need to use the 3-21G basis set first. A stationary point was found as displayed in the item table below.

.log file for this calculation [[Media:LS_NH3_OPT.LOG‎|here]]

<jmolFile text="NH3 molecule optimized with 6-21G(d,p) basis set">LS_nh3_opt.mol2‎</jmolFile>

H-N bond length = 1.01798 A, H-N-H bond angle = 105.744 degrees

[[Image:Nh3_opt_summary.png|center|Summary of results for NH3 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=-1.629729D-09
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3 ====

.log file for this calculation [[Media:LS_NH3_FREQ.LOG‎|here]]

[[Image:Nh3_freq_summary.png|center|Summary of results for NH3 frequency analysis]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000022 0.000450 YES
RMS Force 0.000009 0.000300 YES
Maximum Displacement 0.000078 0.001800 YES
RMS Displacement 0.000039 0.001200 YES
Predicted change in Energy=-1.621683D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -30.7013 -0.0007 0.0006 0.0013 20.2662 28.2997
Low frequencies --- 1089.5562 1694.1246 1694.1863
</pre>

==== MOs of NH3 ====

Link to files on D space: {{DOI|10042/20743}}

==== NBO Analysis of NH3 ====

===== Charge Analysis of NH3 =====

As shown below, the N has a charge of -1.125 and each H has a charge of +0.375

[[Image:LS_nh3_chargeanalysis.png|Charge analysis of NH3 shown by colour]][[Image:LS_nh3_chargeanalysis2.png|Charge analysis of NH3 specific charges]]

=== NH3BH3 ===

==== Optimisation of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_OPT.LOG|here]]

[[Image:LS_nh3bh3_opt_summary.png|center|Summary of results for NH3BH3 optimisation with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000137 0.000450 YES
RMS Force 0.000038 0.000300 YES
Maximum Displacement 0.001013 0.001800 YES
RMS Displacement 0.000223 0.001200 YES
Predicted change in Energy=-1.124453D-07
Optimization completed.
-- Stationary point found.
</pre>

==== Frequency Analysis of NH3BH3 ====

.log file for this calculation [[Media:LS_NH3BH3_FREQ.LOG|here]]

[[Image:LS_nh3bh3_freq_summary.png|center|Summary of results for NH3BH3 frequency analysis with 6-21G basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000264 0.000450 YES
RMS Force 0.000058 0.000300 YES
Maximum Displacement 0.001470 0.001800 YES
RMS Displacement 0.000376 0.001200 YES
Predicted change in Energy=-2.149184D-07
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -8.8883 -0.0004 0.0008 0.0015 19.3593 19.5893
Low frequencies --- 263.3209 631.2464 638.5710
</pre>

=== Energy Comparison ===

* E(NH3) = -26.61532374 a.u.
* E(BH3) = -56.55776856 a.u.
* E(NH3BH3) = 83.22469028 a.u.

(all optimised using 6-31G(d,p) basis set)

* ΔE=E(NH3BH3)-[E(NH3)+E(BH3)] = -0.05159798 a.u.
* Therefore ΔE = -0.05159798/3.8088×10-4 kJ/mol
* ΔE = -135.47kJ/mol

Therefore the bond association energy between B & N in NH3BH3 is -135.47 kJ/mol.

== Ionic Liquids: Designer Solvents (Mini Project) ==

Unless otherwise stated, all the calculations in this section use the 6-21G(d,p) basis set and are carried out on the HPC. (It can be seen how long the calculations would take if they were performed on a normal computer, so long as to be inconvenient!)

=== Part 1: Comparison of Selected "onium" Cations ===

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME4_OPT.mol2</uploadedFileContents>
<text>NMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20757}}

[[Image:LS_nme4_opt_summary.png|center|Summary of results for [N(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000017 0.000300 YES
Maximum Displacement 0.001298 0.001800 YES
RMS Displacement 0.000359 0.001200 YES
Predicted change in Energy=-5.560629D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies below show that the molecule has been optimised to a minimum. The Me-N-Me bond angle is ~109.4 degrees, so the geometry about the central N atom is tetrahedral, which is to be expected.

Link to files on D space: {{DOI|10042/20759}}

[[Image:LS_nme4_freq_summary.png|center|Summary of results for [N(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000073 0.000450 YES
RMS Force 0.000021 0.000300 YES
Maximum Displacement 0.000749 0.001800 YES
RMS Displacement 0.000257 0.001200 YES
Predicted change in Energy=-5.030853D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -13.0303 0.0008 0.0009 0.0012 6.1831 12.0078
Low frequencies --- 179.9148 278.8724 285.7248
</pre>

===== MO Calculations of [N(CH3)4]+ =====

Link to files on D space: {{DOI|10042/20793}}

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''MO #'''
| align="center" style="background:#f0f0f0;"|'''Visualisation'''
| align="center" style="background:#f0f0f0;"|'''Type'''
| align="center" style="background:#f0f0f0;"|'''Description'''
|-
| 6||[[Image:LS_nme4_MO6.png|200px]]||Bonding|| All bonding overlap with the AOs of N and C, it appears that H's MOs are not involved in this at all. There are also through-space interactions between the methyl groups.
|-
| 8||[[Image:LS_nme4_MO8.png|200px]]||Bonding|| Node in the center over the N atom, with a methyl group on either side having bonding interactions. This MO is quite diffuse, it spreads out far from the atoms involved.
|-
| 10||[[Image:LS_nme4_MO10.png|200px]]||Bonding|| All bonding interactions within the 4 methyl groups, but not between them, with what appears an s-AO of the nitrogen in the opposite phase.
|-
| 16||[[Image:LS_nme4_MO16.png|200px]]||Anti-Bonding|| This MO only involves the H AOs, there are 8 nodes so it is strongly antibonding.
|-
| 21 (HOMO)||[[Image:LS_nme4_MO21.png|200px]]||Anti-Bonding|| In this complex MO there are 3 nodes, and it appears to involve AOs from all atoms in the molecule. There is a bonding interaction between one of the methyls and N, and in the opposite phase there are bonding interactions between the other 3 methyls and N. This MO is also quite diffuse, and has anti-bonding interactions between the H atoms on different methyl groups.
|-
|
|}

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

.log file from the NBO analysis [[Media:LS_NME4_NBO.log|here]]

[[Image:LS_nme4_chargeanalysis.png|center|Charge analysis of [NMe4]+]]

The description commonly used that [NR4]+ (where R = alkyl) has the positive charge on the nitrogen is obviously shown to be incorrect by this analysis, the nitrogen is in fact slightly negatively charged and the positive charge is localised on the hydrogens of the alkyl groups. See the excerpt of the .log file below:

<pre>
Natural Population
Natural -----------------------------------------------
Atom No Charge Core Valence Rydberg Total
-----------------------------------------------------------------------
C 1 -0.48341 1.99947 4.46945 0.01449 6.48341
H 2 0.26903 0.00000 0.72996 0.00100 0.73097
H 3 0.26905 0.00000 0.72994 0.00100 0.73095
H 4 0.26908 0.00000 0.72991 0.00100 0.73092
C 5 -0.48341 1.99947 4.46945 0.01449 6.48341
H 6 0.26909 0.00000 0.72991 0.00100 0.73091
H 7 0.26905 0.00000 0.72994 0.00100 0.73095
H 8 0.26903 0.00000 0.72996 0.00100 0.73097
C 9 -0.48344 1.99947 4.46949 0.01449 6.48344
H 10 0.26908 0.00000 0.72992 0.00100 0.73092
H 11 0.26907 0.00000 0.72992 0.00100 0.73093
H 12 0.26906 0.00000 0.72993 0.00100 0.73094
C 13 -0.48328 1.99947 4.46932 0.01449 6.48328
H 14 0.26904 0.00000 0.72996 0.00100 0.73096
H 15 0.26904 0.00000 0.72996 0.00100 0.73096
H 16 0.26901 0.00000 0.72999 0.00100 0.73099
N 17 -0.29510 1.99950 5.28970 0.00591 7.29510
=======================================================================
* Total * 1.00000 9.99736 31.92673 0.07591 42.00000
</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_PME4_OPT.mol</uploadedFileContents>
<text>PMe4+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20761}}

[[Image:LS_pme4_opt_summary.png|center|Summary of results for [P(CH3)4]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000148 0.000450 YES
RMS Force 0.000033 0.000300 YES
Maximum Displacement 0.000959 0.001800 YES
RMS Displacement 0.000312 0.001200 YES
Predicted change in Energy=-1.849677D-07
Optimization completed.
-- Stationary point found.
</pre>

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

Link to files on D space: {{DOI|}}

[[Image:LS_pme4_freq_summary.png|center|Summary of results for [P(CH3)4]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>

</pre>

<pre>

</pre>

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

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

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_SME3_OPT.mol</uploadedFileContents>
<text>SMe3+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20772}}

[[Image:LS_sme3_opt_summary.png|center|Summary of results for [S(CH3)3]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000023 0.000450 YES
RMS Force 0.000010 0.000300 YES
Maximum Displacement 0.001035 0.001800 YES
RMS Displacement 0.000348 0.001200 YES
Predicted change in Energy=-2.234092D-08
Optimization completed.
-- Stationary point found.
</pre>

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

The low frequencies shown below prove that the molecule has been optimised to a minimum. The Me-S-Me bond angles are ~ 102.7 degrees, meaning that the methyl groups are pushed closer together than a "perfect" tetrahedral (i.e. angle < 109 degrees) by the lone pair on S. The geometry is trigonal pyramidal.

Link to files on D space: {{DOI|10042/20774}}

[[Image:LS_sme3_freq_summary.png|center|Summary of results for [S(CH3)3]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000049 0.000450 YES
RMS Force 0.000019 0.000300 YES
Maximum Displacement 0.001590 0.001800 YES
RMS Displacement 0.000520 0.001200 YES
Predicted change in Energy=-3.086772D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -24.9923 -14.4720 -12.1032 -0.0032 -0.0027 -0.0023
Low frequencies --- 158.9980 192.6129 202.1628
</pre>

===== MO Calculations of [S(CH3)3]+ =====

Link to files on D space: {{DOI|10042/20805}}

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

.log file from the NBO analysis [[Media:LS_SME3_NBO.log|here]]

[[Image:LS_sme3_chargeanalysis.png|center|Charge analysis of [SMe3]+]]

=== Part 2: Influence of Functional Groups ===

==== [N(CH3)3(CH2OH)]+ ====

===== Optimisation of [N(CH3)3(CH2OH)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2OH_OPT.mol</uploadedFileContents>
<text>NMe3CH2OH+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20806}}

[[Image:LS_nme3ch3oh_opt_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000074 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.001619 0.001800 YES
RMS Displacement 0.000425 0.001200 YES
Predicted change in Energy=-8.892484D-08
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20810}}

[[Image:LS_nme3ch2oh_freq_summary.png|center|Summary of results for [N(CH3)3(CH2OH)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000066 0.000450 YES
RMS Force 0.000020 0.000300 YES
Maximum Displacement 0.000869 0.001800 YES
RMS Displacement 0.000330 0.001200 YES
Predicted change in Energy=-8.288691D-08
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -4.0940 -0.0002 0.0008 0.0009 12.5644 18.9824
Low frequencies --- 130.9693 217.1689 258.6409
</pre>

===== MO Calculations of [N(CH3)3(CH2OH)]+ =====

Link to files on D space: {{DOI|10042/20814}}

===== NBO Analysis of [N(CH3)3(CH2OH)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2OH_NBO.log|here]]

[[Image:LS_nme3ch2oh_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2OH)]+]]

==== [N(CH3)3(CH2CN)]+ ====

===== Optimisation of [N(CH3)3(CH2CN)]+ =====

Jmol of optimised molecule:
<jmol>
<jmolAppletButton>
<uploadedFileContents>LS_NME3CH2CN_OPT.mol</uploadedFileContents>
<text>NMe3CH2CN+</text>
</jmolAppletButton>
</jmol>

Link to files on D space: {{DOI|10042/20831}}

[[Image:LS_nme3ch2cn_opt_summary.png|center|Summary of results for [N(CH3)3(CH2CN)]+ optimised with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000005 0.000450 YES
RMS Force 0.000002 0.000300 YES
Maximum Displacement 0.000398 0.001800 YES
RMS Displacement 0.000076 0.001200 YES
Predicted change in Energy=-1.565289D-09
Optimization completed.
-- Stationary point found.
</pre>

===== Frequency Analysis of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20839}}

[[Image:LS_nme3ch2cn_freq_summary.png|center|Summary of results for [N(CH3)3(CH2cn)]+ frequency analysis with 6-21G(d,p) basis set]]

<pre>
Item Value Threshold Converged?
Maximum Force 0.000016 0.000450 YES
RMS Force 0.000003 0.000300 YES
Maximum Displacement 0.000391 0.001800 YES
RMS Displacement 0.000100 0.001200 YES
Predicted change in Energy=-1.261257D-09
Optimization completed.
-- Stationary point found.
</pre>

<pre>
Low frequencies --- -0.0008 -0.0005 -0.0001 11.4792 16.4024 17.6028
Low frequencies --- 91.6640 155.1565 217.4529
</pre>

===== MO Calculations of [N(CH3)3(CH2CN)]+ =====

Link to files on D space: {{DOI|10042/20841}}

===== NBO Analysis of [N(CH3)3(CH2CN)]+ =====

.log file from the NBO analysis [[Media:LS_NME3CH2CN_NBO.log|here]]

[[Image:LS_nme3ch2cn_chargeanalysis.png|center|Charge analysis of [N(CH3)3(CH2CN)]+]]

==== Comparison of the 2 Molecules ====

From the NBO analysis of the molecules above, it can be seen that when a hydrogen is replaced with a -OH (electron donating group) then the relative charge on N rises from -0.295 in [N(CH3)4]+ to -0.322, which is more negative i.e. electron density is pushed onto nitrogen.

When the hydrogen is replaced with a -CN group instead (electron withdrawing), then the relative charge on N of -0.295 in [N(CH3)4]+ is decreased to -0.289. i.e. the -CN group has drawn electron density off the central nitrogen making it less negatively charged.

{| class=wikitable border=1
| align="center" style="background:#f0f0f0;"|'''Molecule'''
| align="center" style="background:#f0f0f0;"|'''HOMO'''
| align="center" style="background:#f0f0f0;"|'''LUMO'''
|-
| [N(CH3)4]+||[[Image:LS_nme4_MO21.png|400px]]||[[Image:LS_nme4_MO22.png|400px]]
|-
| [N(CH3)3(CH2OH)]+||[[Image:LS_nme3ch2oh_MO25.png|400px]]||[[Image:LS_nme3ch2oh_MO26.png|400px]]
|-
| [N(CH3)3(CH2CN)]+||[[Image:LS_nme3ch2cn_MO27.png|400px]]||[[Image:LS_nme3ch2cn_MO28.png|400px]]
|}

* Comparisons of the HOMO and LUMO MOs of [N(CH3)4]+, [N(CH3)3(CH2OH)]+ and [N(CH3)3(CH2CN)]+ are shown in the table above.

== References ==
<references/>1