ChemWiki - User contributions [en]

Rep:Module3:JYX08

2011-02-18T16:40:59Z

Jyx08: /* References */

== The Cope Rearrangement ==

[[Image:JYX Cope Rearrangement.JPG|thumb|300px|The Cope Rearrangement]]

The Cope Rearrangement of 1, 5-hexadiene, originally developed by Arthur C. Cope, which specifically involves a [3, 3] sigmatropic shift rearrangement of 1,5-dienes. Although it has been heavily debated whether the mechanism of Cope Rearrangement goes via a concerted, stepwise (two-stage diradical intermediate) or dissociative, but now it is accepted that the rearrangement occurs in a concerted fashion via the either the chair or the boat configuration. In this section of the report[http://www.gaussian.com/ Gaussian]<ref name="Gaussian">Gaussian 09, Revision A.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009: [http://www.gaussian.com/ web]</ref> will be used with [http://en.wikipedia.org/wiki/Hartree-Fock Hartree-Fock (HF)] and [http://en.wikipedia.org/wiki/Density_Functional_Theory density functional theory (DFT)<ref name="DFT">JP. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136''', B864: {{DOI|10.1103/PhysRev.136.B864}}</ref>] methods, to optimise the structures of the [http://en.wikipedia.org/wiki/Transition_state transition states (TS)], in order to locate the low energy transition states hence determine the most preferred mechanism for this reaction.

===Optimisation of 1,5-hexadiene Conformers===
The reactant 1,5-hexadiene can be considered to be in either "gauche" or "anti-periplaner" arrangements based on rotations around the central four carbon atoms. Due to the 6 carbon back bone, multiple Gauche and anti configurations can arise as reported by [http://www.cas.muohio.edu/chm/Faculty/Gung.Htm Gung] and co-workers <ref name="ja00111a016"> B. Gung and co-workers {{DOI|10.1021/ja00111a016}}</ref> that there are twenty seven theoretical conformations. However the symmetry of 1,5-hexadiene and the enantiomerism of the conformations left only 10 possible energetically
distinct conformers. Different gauche and anti-periplanar conformers can be modelled by rotating the dihedral angles created by the alkene units and the central two carbon atoms. Molecules were drawn in Gaussview and each was "cleaned" and then "optimised" by Gaussian at Hartree-Fock(HF)/3-11G level of theory.

The table below shows examples of the optimised structures of the conformers, each with an associated total energy and point group:

{| class="wikitable" border="1"
|- align="center"
|+ Table 1: Conformers of 1,5-hexadiene and their relative energies
!Conformer!!Structure!!Point Group!!Energy/Hartrees!!Relative Energy / kcal/mol!!Log File
|-align="center"
| ''Anti1'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX_anti1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2|| -231.69260 || 0.04 || https://www.ch.ic.ac.uk/wiki/images/d/dc/JYX_anti1_OPT.LOG
|- align="center"
| ''Anti2'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci|| -231.69254 || 0.08 || https://www.ch.ic.ac.uk/wiki/images/b/bb/JYX_anti2_OPT.LOG
|- align="center"
| ''Anti3'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX08_ANTI3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 ||2.25 || https://www.ch.ic.ac.uk/wiki/images/1/1a/JYX_anti3_OPT.LOG
|- align="center"
| ''Gauche2'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX10_GAU2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69166 || 0.62 || https://www.ch.ic.ac.uk/wiki/images/4/40/JYX_GAU2_OPT.LOG
|- align="center"
| ''Gauche4'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX08_GAU4_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 ||-231.69153 || 0.71 || https://www.ch.ic.ac.uk/wiki/images/e/e1/JYX_GAU4_OPT.LOG
|}

===Prediction of the Lowest Energy Conformer===
My initial guess for the lower energy conformer was the ''anti-'' conformer, because the two alkene groups are further apart from each other when the central four carbon atoms are in anti-periplanar conformation. However the calculated results were infact opposite. "Gauche 3" conformer from [[Mod:phys3#Appendix 1|Appendix 1]] was shown to have the lowest energy. This result can be explained in terms of the [http://en.wikipedia.org/wiki/Gauche_effect Gauche effect]. There exists favourable donation of electron density from the πC=C orbital of the C=C double bond into the σ*C-H orbital of the adjacent vinyl proton<ref name="Rocque">B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, ''Mol. Phys.'', 2002, '''100''', 441: {{DOI|10.1080/00268970110081412}}</ref>.

===Further Optimisation of Anti 2 Conformer===
The anti 2 conformer were optimised again using a higher level of theory of B3LYP/6-31G(d). Table below shows the comparison of the two calculations in terms of dihedral angle, bond length and total energy.

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.637°
|118.590°
|3.953°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.654°
|118.594°
|3.904°
|----
|12 bond length/Å
|1.316
|1.334
|0.018
|----
|23 bond length/Å
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length/Å
|1.553
|1.548
|0.005
|----
|Total Energy/HF
| -231.6925
| -234.6117
|2.9192
|----
|}

The reoptimised molecule in terms of the bond length, did not change much, but in terms of the dihedral angle, there is a difference of 4°. The energy of the reoptimised structure was also decreased compare to the molecule optimised by lower level theory by 2.9 a.u.

===Frequency Analysis===
The reoptimised anti- conformer was then taken to run a frequency analysis with the same level of theory. This calculation will give the second derivative of the optimisation. This is useful as it can be used to check if we have indeed fully optimised the conformer. The frequencies must all be positive as this would indicate the minimum point on the energy curve.
The frequency of the molecule was indeed all real and positive ranging from 73 cm-1 to 3233 cm-1.

[[Image:JYX anti2 IR spectrum.jpg|tumb|700px|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

=== Comparison of Energies at 0K and 298K ===
The table of values below are extracted from the Log file. Energies at 0K was recalculated by using the ''Freq=Readisotope'' option in Gaussian.

{|border="1"
|-
!colspan="3"| Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
|align="center"|
!align="center"|Analysis at 298.15K
!align="center"|Analysis at 0K
|-
!align="center"|Sum of electronic and zero-point energies / Eh
|align="center"|-234.46920 a.u.
|align="center"|-234.46877 a.u.
|-
!align="center"|Sum of electronic and thermal energies / Eh
|align="center"|-234.46185 a.u.
|align="center"|-234.46143 a.u.
|-
!align="center"|Sum of electronic and thermal enthalpies / Eh
|align="center"|-234.46091 a.u.
|align="center"|-234.46049 a.u.
|-
!align="center"|Sum of electronic and free energies / Eh
|align="center"|-234.50077 a.u.
|align="center"|-234.50037 a.u.
|}
 

The total energy of the molecule becomes more negative as temperature increases. This is expected since the molecule absorbs more heat at higher temperatures, and thus thermal contribution to the energies increase.

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Optimisation of Chair Transition State===
The chair TS was optimised using HF/3-21G via two types of optimisation.

Opt 1: TS(Berny) Optimisation

Opt 2: A ModRedundant Minimisation with frozen C-C lengths, at 2.20 Å, for the C atoms involved in bond breaking/forming; followed by a TS(Berny) Optimisation with Hessian Derivative calculation for the C-C bond breaking/forming lengths

====Optimisation of Chair Structure using TS(Berny)====
A guessed chair TS structure was drawn on Gaussview using the optimised CH2CHCH2 structure as fragments. The distances in between the terminal carbon atoms in the two fragments were set to be 2.2 Å. The guessed strucuture was optimised to TS(Berny), and a frequency analysis was also done at the same time. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

[[Image:Chairtsvibsmallerjsm108.gif|thumb|center|500px|Illustration of chair imaginary frequency -817.85 cm-1 from optimisation to a TS (Berny)]]

The frequency analysis shows that there is only one imaginary vibration at -817.85 cm-1.
It corrosponds to the bond forming and bond breaking of the [3,3]- sigmatropic rearrangement.
====Optimisation of Chair Structure using Frozen Coordinates====
In this method, the transition structure was generated by freezing the reaction coordinate of the terminal carbon atoms at the bond formation/cleavage positions, and then minimising the rest of the molecule using Opt=ModRedundant. Once the optimisation was done, the reaction coordinate was unfrozen and optimised to a transition state structure.

The table below shows a comparison between the two techniques:

{| class="wikitable" border="1"
|+ ''Optimisation of Chair TS''
! Properties !! ''TS(Berny)'' !! ''Frozen Coordinate''
|-
| Final Energy / a.u. ||align="center"| -231.61933 ||align="center"| -231.61932
|-
| Final Energy / kJ mol-1 ||align="center"| -608116.0 ||align="center"| -608116.5
|-
| Imaginary Frequency / cm-1 ||align="center"| -817.85 ||align="center"| -818.21
|-
| C-C Bond Breaking/Forming Length / Å ||align="center"| 2.02 ||align="center"| 2.02
|}

As we can see from the table above, both technique gave very similar results, which means both methods are reliable enough for this calculation.

===Boat Transition State Optimisation===
The boat transition state was found using the QST2 method. The Ci anti 2 conformer was copied into a new window, and then pasted as "add molgroup". The reactant and product were then numbered corresponding to the reaction:

[[Image:JYX_BoatTS.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

This was then sent to be optimised to a TS (QST2). The job failed to converge and so the reactant and product were altered manually so that they resemble the boat transition structure. The central C-C-C-C dihedral angle was changed to 0°, whilst the central C-C-C angles were changed to 100°. The TS (QST2) optimisation was then set up again.

The imgainary frequency was obtained at -840 cm-1

Optimised distance between the terminal ends of the allyl fragments was 2.13640 Å

Energy of transition state was -231.60280217 Hartrees

==References==
<references/>

Rep:Module3:JYX08

2011-02-18T16:40:27Z

Jyx08: /* Boat Transition State Optimisation */

Rep:Module3:JYX08

2011-02-18T16:26:42Z

Jyx08: /* Boat Transition State Optimisation */

File:JYX BoatTS.gif

2011-02-18T16:20:09Z

Jyx08:

Rep:Module3:JYX08

2011-02-18T15:52:46Z

Jyx08: /* Optimisation of Chair Structure using Frozen Coordinates */

Rep:Module3:JYX08

2011-02-18T15:51:47Z

Jyx08: /* Optimisation of Chair Structure using TS(Berny) */

Rep:Module3:JYX08

2011-02-18T15:22:52Z

Jyx08: /* Chair */

== The Cope Rearrangement ==

[[Image:JYX Cope Rearrangement.JPG|thumb|300px|The Cope Rearrangement]]

The Cope Rearrangement of 1, 5-hexadiene, originally developed by Arthur C. Cope, which specifically involves a [3, 3] sigmatropic shift rearrangement of 1,5-dienes. Although it has been heavily debated whether the mechanism of Cope Rearrangement goes via a concerted, stepwise (two-stage diradical intermediate) or dissociative, but now it is accepted that the rearrangement occurs in a concerted fashion via the either the chair or the boat configuration. In this section of the report[http://www.gaussian.com/ Gaussian]<ref name="Gaussian">Gaussian 09, Revision A.1, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009: [http://www.gaussian.com/ web]</ref> will be used with [http://en.wikipedia.org/wiki/Hartree-Fock Hartree-Fock (HF)] and [http://en.wikipedia.org/wiki/Density_Functional_Theory density functional theory (DFT)<ref name="DFT">JP. Hohenberg, W. Kohn, ''Phys. Rev.'', 1964, '''136''', B864: {{DOI|10.1103/PhysRev.136.B864}}</ref>] methods, to optimise the structures of the [http://en.wikipedia.org/wiki/Transition_state transition states (TS)], in order to locate the low energy transition states hence determine the most preferred mechanism for this reaction.

===Optimisation of 1,5-hexadiene Conformers===
The reactant 1,5-hexadiene can be considered to be in either "gauche" or "anti-periplaner" arrangements based on rotations around the central four carbon atoms. Due to the 6 carbon back bone, multiple Gauche and anti configurations can arise as reported by [http://www.cas.muohio.edu/chm/Faculty/Gung.Htm Gung] and co-workers <ref name="ja00111a016"> B. Gung and co-workers {{DOI|10.1021/ja00111a016}}</ref> that there are twenty seven theoretical conformations. However the symmetry of 1,5-hexadiene and the enantiomerism of the conformations left only 10 possible energetically
distinct conformers. Different gauche and anti-periplanar conformers can be modelled by rotating the dihedral angles created by the alkene units and the central two carbon atoms. Molecules were drawn in Gaussview and each was "cleaned" and then "optimised" by Gaussian at Hartree-Fock(HF)/3-11G level of theory.

The table below shows examples of the optimised structures of the conformers, each with an associated total energy and point group:

{| class="wikitable" border="1"
|- align="center"
|+ Table 1: Conformers of 1,5-hexadiene and their relative energies
!Conformer!!Structure!!Point Group!!Energy/Hartrees!!Relative Energy / kcal/mol!!Log File
|-align="center"
| ''Anti1'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX_anti1_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2|| -231.69260 || 0.04 || https://www.ch.ic.ac.uk/wiki/images/d/dc/JYX_anti1_OPT.LOG
|- align="center"
| ''Anti2'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX_ANTI2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || Ci|| -231.69254 || 0.08 || https://www.ch.ic.ac.uk/wiki/images/b/bb/JYX_anti2_OPT.LOG
|- align="center"
| ''Anti3'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX08_ANTI3_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2h || -231.68907 ||2.25 || https://www.ch.ic.ac.uk/wiki/images/1/1a/JYX_anti3_OPT.LOG
|- align="center"
| ''Gauche2'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX10_GAU2_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 || -231.69166 || 0.62 || https://www.ch.ic.ac.uk/wiki/images/4/40/JYX_GAU2_OPT.LOG
|- align="center"
| ''Gauche4'' || <jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>JYX08_GAU4_OPT.mol</uploadedFileContents>
</jmolApplet></jmol> || C2 ||-231.69153 || 0.71 || https://www.ch.ic.ac.uk/wiki/images/e/e1/JYX_GAU4_OPT.LOG
|}

===Prediction of the Lowest Energy Conformer===
My initial guess for the lower energy conformer was the ''anti-'' conformer, because the two alkene groups are further apart from each other when the central four carbon atoms are in anti-periplanar conformation. However the calculated results were infact opposite. "Gauche 3" conformer from [[Mod:phys3#Appendix 1|Appendix 1]] was shown to have the lowest energy. This result can be explained in terms of the [http://en.wikipedia.org/wiki/Gauche_effect Gauche effect]. There exists favourable donation of electron density from the πC=C orbital of the C=C double bond into the σ*C-H orbital of the adjacent vinyl proton<ref name="Rocque">B.G. Rocque, J.M. Gonzales, H.F. Schaefer III, ''Mol. Phys.'', 2002, '''100''', 441: {{DOI|10.1080/00268970110081412}}</ref>.

===Further Optimisation of Anti 2 Conformer===
The anti 2 conformer were optimised again using a higher level of theory of B3LYP/6-31G(d). Table below shows the comparison of the two calculations in terms of dihedral angle, bond length and total energy.

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.637°
|118.590°
|3.953°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.654°
|118.594°
|3.904°
|----
|12 bond length/Å
|1.316
|1.334
|0.018
|----
|23 bond length/Å
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length/Å
|1.553
|1.548
|0.005
|----
|Total Energy/HF
| -231.6925
| -234.6117
|2.9192
|----
|}

The reoptimised molecule in terms of the bond length, did not change much, but in terms of the dihedral angle, there is a difference of 4°. The energy of the reoptimised structure was also decreased compare to the molecule optimised by lower level theory by 2.9 a.u.

===Frequency Analysis===
The reoptimised anti- conformer was then taken to run a frequency analysis with the same level of theory. This calculation will give the second derivative of the optimisation. This is useful as it can be used to check if we have indeed fully optimised the conformer. The frequencies must all be positive as this would indicate the minimum point on the energy curve.
The frequency of the molecule was indeed all real and positive ranging from 73 cm-1 to 3233 cm-1.

[[Image:JYX anti2 IR spectrum.jpg|tumb|700px|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

=== Comparison of Energies at 0K and 298K ===
The table of values below are extracted from the Log file. Energies at 0K was recalculated by using the ''Freq=Readisotope'' option in Gaussian.

{|border="1"
|-
!colspan="3"| Thermochemistry data from frequency analysis of 6-31G(d)-optimized 1,5-hexadiene
|-
|align="center"|
!align="center"|Analysis at 298.15K
!align="center"|Analysis at 0K
|-
!align="center"|Sum of electronic and zero-point energies / Eh
|align="center"|-234.46920 a.u.
|align="center"|-234.46877 a.u.
|-
!align="center"|Sum of electronic and thermal energies / Eh
|align="center"|-234.46185 a.u.
|align="center"|-234.46143 a.u.
|-
!align="center"|Sum of electronic and thermal enthalpies / Eh
|align="center"|-234.46091 a.u.
|align="center"|-234.46049 a.u.
|-
!align="center"|Sum of electronic and free energies / Eh
|align="center"|-234.50077 a.u.
|align="center"|-234.50037 a.u.
|}
 

The total energy of the molecule becomes more negative as temperature increases. This is expected since the molecule absorbs more heat at higher temperatures, and thus thermal contribution to the energies increase.

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Optimisation of Chair Transition State===
The chair TS was optimised using HF/3-21G via two types of optimisation.

Opt 1: TS(Berny) Optimisation

Opt 2: A ModRedundant Minimisation with frozen C-C lengths, at 2.20 Å, for the C atoms involved in bond breaking/forming; followed by a TS(Berny) Optimisation with Hessian Derivative calculation for the C-C bond breaking/forming lengths

====Optimisation of Chair Structure using TS(Berny)====
A guessed chair TS structure was drawn on Gaussview using the optimised CH2CHCH2 structure as fragments. The distances in between the terminal carbon atoms in the two fragments were set to be 2.2 Å. The guessed strucuture was optimised to TS(Berny), and a frequency analysis was also done at the same time. The optimisation was set up so that the force constants were only calculated once with additional keywords, Opt=NoEigen, which prevents the calculation from crashing if more than one imaginary frequency is detected during the optimisation.

[[Image:Chairtsvibsmallerjsm108.gif|thumb|center|500px|Illustration of chair imaginary frequency -817.85 cm-1 from optimisation to a TS (Berny)]]

The frequency analysis shows that there is only one imaginary vibration at -817.85 cm-1.
It corrosponds to the bond forming and bond breaking of the [3,3]- sigmatropic rearrangement.

The table below shows a comparison between the two techniques:

File:JYX chairTS 818.gif

2011-02-18T15:10:41Z

Jyx08:

Rep:Module3:JYX08

2011-02-18T15:00:52Z

Jyx08: /* Comparison of Energies at 0K and 298K */

Rep:Module3:JYX08

2011-02-18T14:58:29Z

Jyx08: /* Comparison of Energies at 0K and 298K */

Rep:Module3:JYX08

2011-02-18T14:52:23Z

Jyx08: /* Comparison of Energies at 0K and 298K */

Rep:Module3:JYX08

2011-02-18T14:45:58Z

Jyx08: /* Comparison of Energies at 0K and 298K */

Rep:Module3:JYX08

2011-02-16T05:57:46Z

Jyx08: /* Frequency Analysis */

Rep:Module3:JYX08

2011-02-16T05:57:18Z

Jyx08: /* Frequency Analysis */

Rep:Module3:JYX08

2011-02-16T05:26:10Z

Jyx08: /* Further Optimisation of Anti 2 Conformer */

File:JYX anti2 IR spectrum.jpg

2011-02-16T05:20:10Z

Jyx08:

File:JYX ANTI2 FREQ ANALYSIS.LOG

2011-02-16T05:14:52Z

Jyx08:

Rep:Module3:JYX08

2011-02-16T03:48:28Z

Jyx08: /* Further Optimisation of Anti 2 Conformer */

Rep:Module3:JYX08

2011-02-16T03:32:17Z

Jyx08: /* Further Optimisation of Anti 2 Conformer */

Rep:Module3:JYX08

2011-02-16T03:28:35Z

Jyx08: /* Prediction of the Lowest Energy Conformer */

Rep:Module3:JYX08

2011-02-16T03:05:07Z

Jyx08: /* Optimisation of 1,5-hexadiene Conformers */

Rep:Module3:JYX08

2011-02-16T01:50:24Z

Jyx08: /* Optimisation of 1,5-hexadiene Conformers */

Rep:Module3:JYX08

2011-02-16T01:48:04Z

Jyx08: /* Optimisation of 1,5-hexadiene Conformers */

File:JYX10 GAU2 OPT.mol

2011-02-16T01:45:53Z

Jyx08:

File:JYX09 GAU2 OPT.mol

2011-02-16T01:30:59Z

Jyx08:

File:JYX08 GAU4 OPT.mol

2011-02-16T01:29:17Z

Jyx08:

File:JYX08 GAU2 OPT.mol

2011-02-16T01:28:45Z

Jyx08:

File:JYX08 ANTI3 OPT.mol

2011-02-16T01:27:18Z

Jyx08:

Rep:Module3:JYX08

2011-02-16T01:20:22Z

Jyx08: /* Optimisation of 1,5-hexadiene Conformers */

File:JYX GAU4 OPT.LOG

2011-02-16T01:12:04Z

Jyx08:

File:JYX GAU2 OPT.mol

2011-02-16T01:08:36Z

Jyx08:

File:JYX GAU2 OPT.LOG

2011-02-16T01:07:10Z

Jyx08:

File:JYX ANTI3 OPT.mol

2011-02-16T01:03:20Z

Jyx08:

File:JYX ANTI3 OPT.LOG

2011-02-16T01:02:05Z

Jyx08:

File:JYX ANTI2 OPT.mol

2011-02-16T00:58:32Z

Jyx08:

File:JYX ANTI2 OPT.LOG

2011-02-16T00:57:37Z

Jyx08:

File:JYX anti1 OPT.mol

2011-02-16T00:45:54Z

Jyx08:

File:JYX anti1 OPT.LOG

2011-02-16T00:44:35Z

Jyx08:

Rep:Module3:JYX08

2011-02-15T20:26:53Z

Jyx08: /* The Cope Rearrangement */

Rep:Module3:JYX08

2011-02-15T19:00:41Z

Jyx08: /* Optimisation of Reactants and Products */

Rep:Module3:JYX08

2011-02-15T15:50:05Z

Jyx08: /* The Cope Rearrangement */

Rep:Module3:JYX08

2011-02-13T18:22:03Z

Jyx08: /* The Cope Rearrangement */

Rep:Module3:JYX08

2011-02-13T18:21:30Z

Jyx08: /* The Cope Rearrangement */

Rep:Module3:JYX08

2011-02-13T18:14:52Z

Jyx08: New page: == The Cope Rearrangement == The Cope Rearrangement The Cope Rearrangement of 1, 5-hexadiene, originally developed by Arthur C. Cope, whi...

File:JYX Cope Rearrangement.JPG

2011-02-13T18:14:17Z

Jyx08:

Rep:Module2:JYX08

2011-02-08T16:59:13Z

Jyx08: /* Frequency Analysis */

=Part I: Small Molecule Optimisation=

==BH3==

===Optimisation===

BH3 is optimised using Gaussian, this was done using the B3LYP method with basis set of 3-21G. This is a rather "simple" basis set. It works well when it is applied to small molecules, when it is applied to large or complicated molecules will result in an inaccurate calculation. However, for this calculation for BH3, it is enough to obtain a good approximation. The molecule was drawn in Gaussview, and each BH bond was adjusted to 1.5Å first in prior of taking the optimisation to set ourselves a good starting point.

A summary of the optimisation is shown in the table below:

{| class="wikitable" border="1"
|+ ''Table. 1'' '''BH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3jyx.mol</uploadedFileContents>
<text>BH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|3-21G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -26.4622 a.u (-69.475 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|10.0 sec
|----
|B-H Bond length
|1.19Å
|----
|HBH Bond angle
|120.0°
|----
|}

The log file can be viewed here: https://www.ch.ic.ac.uk/wiki/images/4/46/BH3_OPTJYX.LOG

As we can see here, the optimised bond length is 1.19Å while the bond angle is 120.0°, which agrees well with the literature<ref name="j.jssc.2007.01.031"> M. R. Hartman, J. J. Rush, T. J. Udovic, R. C. Bowman Jr and S. J. Hwang ''J. Solid State. Chem.'', 2007, '''180''', 1298 - 1305 {{DOI|10.1016/j.jssc.2007.01.031}}</ref> experimental observations, which has proven that BH3 adopts a trigonal planar structure of bond length 1.21Å and bond angle 120.0°.

The RMS and Energy curves can be viewed after the run. The graphs represent the change in energy and RMS gradient against the calculation step. As the RMS gradient converges to 0, means that the total energy is minimised and the geometry of the molecule is therefore fully optimised.
[[Image:JyxBh3optgraph.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
We can see from the graph above, that it took 5 steps of calculation for the geometry of BH3 to be fully optimised, and the gradient has successfully converged to 0.

===Molecular Orbital Analysis===
The molecular orbital of BH3 was generated computationally. The result of this was then compared with the predicted molecular orbitals using linear combination of atomic orbitals (LCAO) method, and the two were found matches quite well. This indicates that the qualitative MO theory is quite accurate in terms of determining the shape of the MOs. However the downside is that it cannot predict the energies for the MOs quantitatively as the computational method.

The comparison of the MOs are shown below:

[[Image:Jyx BH3 MO.gif]]

The job was published in D-space: http://hdl.handle.net/10042/to-6885

=== NBO Analysis ===
{|align="right"
|-
|[[Image:BH3-NMO.jpg|thumb|200px|left|NBOanalysis: colour by charge of BH3]]

|}

The Natural Bond Orbital (NBO) analysis investigates the charge distribution in a molecule. From the log file, the overall charge is zero as we expect. All three of the H atoms have full s orbital contribution, where as for B atom, it has 33% contribution from the s, and 66% from the p orbitals. The colour appeared on the molecule corresponds to the charge distribution in this molecule. Bright green indicates highly positive charge and bright red highly negative charge. As expected the boron atom which is Lewis deficient is highly positively charged.

===Vibrational Analysis===
On the optimised BH3 molecule, a frequency analysis was performed:

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/3/33/JYX_BH3_FREQ.LOG
{| class="wikitable" border="1"
|+ ''Table. 2'' '''BH3 Vibration Frequencies & Modes'''
|'''Mode'''
|'''Vibration'''
|'''Description'''
|'''Freq/cm-1'''
|'''Intensity'''
|'''Symmetry (D3h)'''
|'''Literature Freq /cm-1<ref name="Schuurman">M.S. Schuurman, W.D. Allen, H.F. Schaefer III, ''J. Comput. Chem.'', 2005, '''26''', 1106: {{DOI|10.1002/jcc.20238}}</ref>'''
|----
|1
|[[Image:JYX_BH3_vib1.gif|centre]]
|'''Out of plane wagging''': All H move in direction of arrow while B moves in the opposite direction.
|1145.7
|92.7
|A2"
|1159
|----
|2
|[[Image:JYX_BH3_vib2.gif|centre]]
|'''In-plane Scissoring''': 2 H move in the scissors-like fashion while B and the third H moves downwards as one unit, away from the 2H's.
|1205
|12.4
|E'
|1204.7
|----
|3
|[[Image:JYX_BH3_vib3.gif|centre]]
|'''In-plane Rocking''': 2H and B rock concertedly in plane as one unit, while the third H swings in opposite direction with larger amplitude.
|1205
|12.4
|E'
|1204.7
|----
|4
|[[Image:JYX_BH3_vib4.gif|centre]]
|'''Symmetric Stretching''': All three H move away from B within the BH3 plane, while the central B remains still.
|2592.8
|0
|A1'
|NA
|----
|5
|[[Image:JYX_BH3_vib5.gif|centre]]
|'''Asymmetric stretching''': two H moves, one away from the B center, and the other one comes towards B wagging in the plane of the molecule, while the third H remains still.
|2731.3
|103.8
|E'
|2616
|----
|6
|[[Image:JYX_BH3_vib6_1.gif|centre]]
|'''Asymmetric stretching''': two H move away (or toward) B in concerted motion, while third H moves towards (or in -- opposite to the two H), all in the plane of screen. B moves towards and away from this third H.
|2731.3
|103.8
|E'
|2616
|----
|}

After the vibrational frequency analysis was done, a predicted vibrational spectrum can be viewed.
[[Image:Jyx_BH3_IRspectrum.jpg|none|frame|Predicted IR Spectrum of BH3]]

From the vibrational frequency analysis, 6 vibrational modes were identified. However from the graph above, only 5 peaks can be oberved. This is due to the vibrational spectrum is highly dependent on the symmetry hence the dipole moments of the vibration modes. Therefore for symmetric vibrations, i.e. for vibration 4, due to the overall dipole moment is cancelled out by individual stretches, hence it does not appear on the IR spectrum.

==TlBr3==
===Optimisation===

The structure of TlBr3 was optimised again by Gaussian, the method we employed this time was slightly different from the one we used to carry out the optimisation for BH3. We have used a higher level of basis set (LanL2DZ) due to the heavier atoms being present.

Log file for the optimisation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/a/ab/Jyx_TLBR3_OPTIMISATION.LOG

{| class="wikitable" border="1"
|+ ''Table.3'' '''TlBr3 Optimisation''' <jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Tlbr3.mol</uploadedFileContents>
<text>TlBr3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|LANL2DZ
|----
|Charge
|0
|----
|Spin
|single
|----
|E(RB+HF-LYP)
| - 91.2181 a.u (-239.264 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|34.0 sec
|----
|Tl-Br bond length
|2.58Å
|----
|Br-Tl-Br angle
|120.0°
|----
|}
Bond length reported in literature<ref name="TBr3">J. Glaser, ''Acta Chem. Scand. A'', 1979, '''33''', 789</ref> is 2.52Å and bond angle is 120.0Å, which agrees well with calculated values obtained, the bond angle in our model also obeys the ideal geometry of a trigonal planar compound. Slight deviations could be accounted for, that the simulated conditions done by Gaussian are different from the conditions of measurement done experimentally.

[[Image:Jyx_RMS-gradient-total-energy-graph-tlbr3.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
From the graph above, we can see that the gradient has successfully converged to 0, and the total energy is also minimised, which corresponds to the most stable geometry of the molecule.

===Vibrational Analysis===

The log file can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/e/e3/Jyx_TLBR3_FREQUENCY.LOG
Vibration frequency analysis was done using the same method and basis set as we used to optimise the structure. This is essential as to ensure the results maintaining accuracy and consistency.

*Low frequencies reported in the log file for this calculations are: -3.4226 -0.0026 -0.0004 0.0015 3.9361 3.9361
*Real low frequencies actually start at: 46.4288 46.4291 52.1449

{| class="wikitable" border="1"
|+ ''Table.4'' Vibrational Frequencies of TlBr3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:Jyxtlbr3v1.png|right]]||'''In-Plane Scissoring''': 2 Br atoms move towards and away from each other in a in-phase motion, the other Br atom and the Tl atom move away from the scissor in the TlBr3 plane at a smaller amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:Jyxtlbr3v2.png|right]]||'''In-Plane Rocking''': 2 Br atoms and the Tl atom rock in the TlBr3 plane in a in-phase motion with the Tl not being completely stationary, while the Br atom at the top swings at a larger amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:Jyxtlbr3v3.png|right]]||'''Out-of-Plane Wagging''': All 3 Br atoms move together in a in-phase motion in and out of the TlBr3 plane , the Tl atom wagging out of phase at a smaller amplitude ||align="center"| 52.1 ||align="center"| 5.8 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:Jyxtlbr3v4.png|right]]||'''Symmetric Stretching''': the Tl atom remains stationary, while the Br atoms move towards and away from the Tl atom in the TlBr3 plane in a in-phase motion, ||align="center"| 165.3 ||align="center"| 0 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:Jyxtlbr3v5.png|right]]||'''Asymmetric Stretching''': the top Br atom remains stationary, while the other 2 Br atoms move towards and away from the Tl atom in the TlBr3 plane in a out-of-phase motion, and the Tl atom wags between the two atoms at a small amplitude. ||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:Jyxtlbr3v6.png|right]]||'''Asymmetric Stretching''': the top Br atoms oscillates out-of-phase with the other 2 Br atoms, towards and away from the Tl atom in the TlBr3 plane, while the Tl move towards and away from the top Br atom in concerted motion .||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|}

[[Image:JYX_TlBr3_-_IR_spec.jpg|centre]]

For symmetrical molecules, 3N-6 vibrational modes should be present, where N is the number of atoms. For non-symmetrical molecule, 3N-5 vibrational modes should be seen. Therefore, for both BH3 and TlBr3 symmetrical compounds, 6 vibrational modes should be observed, corresponding to Gaussian calculated results. However from the spectrum, only 3 peaks can be observed. This is due to two of the peaks corresponds to degenerate vibration motions, and there is also a symmetric vibration mode which will not be observed from the spectrum.

====Why Do a Frequency Analysis?====

In the optimisation step, the derivative of the total energy curve has reached zero. However this does not indicate whether it is a maximum or a minimum turning point. The frequency analysis is essentially the second derivative of the curve. It is important that all values we obtained need to be positive in order to confirm that it is a minimum turning point. Any negative values would indicate maximum turning point being present, and thus optimisation has failed.

====Missing Bonds in Guassview====

Some molecules after being optimised by Gaussian, some of the bonds have disappeared. This doesn't not mean that there is no bonds between the atoms, it simply means that the bond length has exceeded the limit that was originally set for Gaussview. Thus Gaussview does not recognise this as a bonding interaction, hence does not draw the bonds in, but there are certainly bonding interactions present.

====Definition of a Bond====

A bond would be regard as a force of attraction between two or more atoms which stabilise the energy of the system. Sufficient overlap of orbitals of at least two atoms would result in formation of a bond. Bonding can also be described as a result of electromagnetic interaction between positively charged nuclei and negatively charged shared electrons (covalent bond), electrostatic interaction due to large difference in electronegativity(ionic bond).

=Part II: An Organometallic Complex=

==Mo(CO)4(PCl3)2 Cis-Trans Isomerism==

===Optimisation===
The cis and trans isomers of Mo(CO)4(PCl3)2 are optimised by the method B3LYP in Gaussian. They were pre-optimised using the pseudo potential/basis set of LanL2MB to get close to the structure with the minimal energy (opt=loose), and subsequently optimised a second time while manually rotated the bonds to force the molecule in a geometry close to the low energy conformation, with the pseudo potential being LanL2DZ. Pseudo potentials are applied here to provide a higher level of optimisation for these heavier atoms. LanL2DZ is an even higher level optimisation than LanL2MB, more suited to this large complex with heavy atoms like Mo.

{| class="wikitable" border="1"
|+ ''Table.5'' '''Mo(CO)4(PCl3)2 Optimisation'''
|'''''(1st optimisation)'''''
|
|
|----
|
|'''cis-isomer'''
|'''trans-isomer'''
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-rough.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx-Stagg-trans-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6894}}
|{{DOI|10042/to-6893}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2MB
|LANL2MB
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| - 617.5252 au (-1637.923 kJ/mol)
| - 617.5221 au (-1637.915 kJ/mol)
|----
|Dipole Moment
|8.42 Debye
|0.00 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|10min 56sec
|03min 07sec
|----
|'''''(2nd optimisation)'''''
|
|
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-modified.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Trans-eclips-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6895}}
|{{DOI|10042/to-6896}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2DZ
|LANL2DZ
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| -623.5771 a.u. (-1653.976 kJ/mol)
| -623.5760 a.u. (-1653.973 kJ/mol)
|----
|Dipole Moment
|1.31 Debye
|0.31 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|18min 38sec
|11min 38sec
|----
|}

Looking solely at the second optimisation, the energy of the cis isomer is ~3Jmol-1 higher than for the trans isomer, which means that the trans isomer is a thermodynamically favoured structure in relative to the cis isomer. This effect can be rationalised in terms of the steric effects. The PCl3 group can be considered relatively bulky and spatially demanding. The molecule will be in its low energy state when two groups are kept as far apart as possible in a trans geometry. This theory was in fact backed up by the experimental observation reported in a literature paper <ref name="Mo_trans">D. J. Darensbourg, ''Inorg. Chem.'', 1979, '''18''', 14. {{DOI|10.1021/ic50191a003}}</ref>. However the trans-isomer is no longer perfectly symmetric after the second optimisation. The bond angle between the two trans P groups has shifted from 180° to 177.4°, which the molecule results in having a very slight dipole moment of 0.31 Debye. The Mo-C bond has a distance of 2.06 Å and Mo-P with a distance of 2.44 Angstroms(corresponding well with 2.5Å in literature <ref>Structural characterizations of cis-Mo(CO)4(PPhMe2)(NHC5H10) and cis-Mo(CO)4(PPhMe2)(PPh3) and their solution reactivities toward carbon monoxide F. Albert. Cotton, Donald J. Darensbourg, Simonetta. Klein, Brian W. S. Kolthammer, Inorg. Chem., 1982, 21 (4), pp 1651–1655. Inorganica Chimica Acta, Volume 254, Issue 1, 1 January 1997, Pages 167-171, Crystal structures of trans-[Mo(CO)4(PPh3)2] and 1,4-bis (diphenylphosphino)-2,5-difluorobenzene, Graeme Hogarth and Tim Norman</ref>). In the case of cis-isomer, Mo-C bond length is about 2.06Å and Mo-P is ~2.51Å .

''Table.6'' Geometry data of trans-isomer compared to literature values
{| width="70%" border="1"
|-
| align="center" |
| align="center" |lit.<ref name="translit">D. W. Bennett, T. A. Siddiquee, D. T. Haworth, S. E. Kabir, F. K. Camellia, ''J. Chem. Crys.'', '''2004''', ''34'', 353-359.{{DOI|10.1023/B:JOCC.0000028667.12964.28}}</ref> trans [Cr(CO)4(PPh3)2]
| align="center" | trans [Mo(CO)4(PCl3)2]
|-
| align="left" | mean Mo-P bond length / Å
| align="center" | 2.36
| align="center" | 2.44
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 1.87
| align="center" | 2.06
|-
| align="left" | P-Mo-P bond angle/ °
| align="center" | 176.7
| align="center" | 177.4
|-
| align="left" | P-Mo-C bond angle / °
| align="center" | 89.5
| align="center" | 90(averaged)
|}
''Table.7'' Geometry data of cis-isomer compared to literature value
{| width="70%" border="1"
|-
| align="left" |
| align="center" |lit.<ref name="cislit">D. J. Darensbourg, R. L. Kump, ''Inorg. Chem.'', '''1978''', ''17'', 2680-2682. {{DOI|10.1021/ic50187a062}}</ref> cis [Mo(CO)4(PPh3)2]
| align="center" | cis [Mo(CO)4(PCl3)2]
|-
| align="left" | mean P-Mo bond length / Å
| align="center" | 2.51
| align="center" | 2.48
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 2.03
| align="center" | 2.03
|-
| align="left" | P-Mo-P bond angle / °
| align="center" | 94.2
| align="center" | 95.6
|-
| align="left" | P-Mo-C (trans to P) bond angle / °
| align="center" | 176.1
| align="center" | 174.4
|-
| align="left" | P-Mo-C (cis to P) bond angle/ °
| align="center" | 90.1
| align="center" | 87.3
|}

From the table above, the calculated data values agrees well with the literature.

===Frequency/IR analysis===

Trans frequency output file on D-space: |{{DOI|10042/to-6942}}
Cis frequency output on D-space: |{{DOI|10042/to-6941}}

All the low frequencies are positive which indicates that both molecule are at the energy minima, and the geometry is successfully optimised.

The low frequencies vibrations of both Mo(CO)4(PCl3)2 isomers are shown below:

{| class="wikitable" border="1"
|+ '''Table.8''' Low frequencies vibrations of both Mo(CO)4(PCl3)2 Isomers
! Isomer !!width="400"| Form of Vibration !! Frequency / cm-1 !! Intensity !! Symmetry (C1 Point Group)
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v1.jpg|150px|center]]||align="center"| 4.98 ||align="center"| 0.01 ||align="center"| A
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v2.jpg|150px|center]]||align="center"| 6.13 ||align="center"| 0.00 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v1.jpg|150px|center]] ||align="center"| 10.73 ||align="center"| 0.0264 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v2.jpg|150px|center]] ||align="center"| 17.62 ||align="center"| 0.0074 ||align="center"| A
|}

The carbonyl stretch vibrations are shifted about 40-50 cm-1, this is because the triphophine groups used in the experimental measurement are now replaced by PCl3 for this calculation. Due to symmetry of the vibrations for the trans-isomer, there are 2 IR inactive modes which does not appear on the spectrum.
{| class="wikitable" border="1"
|+ '''Table.9''' Carbonyl Stretching Frequencies of Mo(CO)4(PCl3)2''
! Isomer !! Calculated Frequency / cm-1 !! Calculated Intensity !! Experimental Frequency !! Point Group (C2v Symmetry)<ref name="Cotton">F.A. Cotton, ''Inorg. Chem.'', 1964, '''3''', 702: {{DOI|10.1021/ic50015a024}}</ref>
|-
|align="center"| cis ||align="center"| 1945.3 ||align="center"| 762.7 ||align="center"| 1986 ||align="center"| B2
|-
|align="center"| cis ||align="center"| 1948.7 ||align="center"| 1948.5 ||align="center"| 1994||align="center"| B1
|-
|align="center"| cis ||align="center"| 1958.3 ||align="center"| 633.0 ||align="center"| 2004 ||align="center"| A1
|-
|align="center"| cis ||align="center"| 2023.3 ||align="center"| 597.5 ||align="center"| 2072 ||align="center"| A1
|-
|align="center"| trans ||align="center"| 1950.5 ||align="center"| 1475.4 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1951.1 ||align="center"| 1466.7 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1977.4 ||align="center"| 0.63 ||align="center"| - ||align="center"| B1g
|-
|align="center"| trans ||align="center"| 2031.1 ||align="center"| 3.8 ||align="center"| - ||align="center"| A1g
|}

{| align="center" width="100%" border="0"
|-
| align="center" |[[Image:Trans-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of trans-isomer]]
| align="center" |[[Image:Cis-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of cis-isomer]]
|}

All four CO vibrations were observed in the spectrum for the cis-isomer, while only one peak was obersved for the trans-isomer due to the degenerate vibration states, thus only one CO stretch peak was seen for the IR spectrum of the trans-isomer.

=Part III: Mini-Project=

==NH3==
===Optimisation===

{| class="wikitable" border="1"
|+ ''Table. 10'' '''NH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>JyxNH3_OPT.mol</uploadedFileContents>
<text>NH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|6-31G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -56.531 a.u (-43.402 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|C3
|----
|Job cpu time
|12.0 sec
|----
|B-H Bond length
|1.006Å
|----
|HBH Bond angle
|116.251°
|----
|}

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/f/fa/JyxNH3_OPT.LOG‎
[[Image:JyxNH3_optimisation_graph.jpg]]

===MO Analysis===
Log file for this calculation can be viewed here:{{DOI|10042/to-7047}}
{| {{table}} border="1" style="text-align:center; border:1px solid black;"
| align="center" style="background:#f0f0f0;"|'''Orbital'''
| align="center" style="background:#f0f0f0;"|'''MO of NH3'''
| align="center" style="background:#f0f0f0;"|'''MO of BH3'''
|-
| A1'||[[Image:Jyx-NH3_MO2.jpg|200px]]||[[Image:SJCryer_MO_2.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO4.jpg|200px]]||[[Image:SJCryer_MO_3.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO3.jpg|200px]]||[[Image:SJCryer_MO_4.jpg|230px]]
|-
| A2<nowiki>"</nowiki>||[[Image:Jyx-NH3_MO5.jpg|200px]]||[[Image:SJCryer_MO_5.jpg|230px]]
|-
| A1'||[[Image:Jyx-NH3_MO6.jpg|200px]]||[[Image:SJCryer_MO_6.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO7.jpg|200px]]||[[Image:SJCryer_MO_7.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO8.jpg|200px]]||[[Image:SJCryer_MO_8.jpg|230px]]
|}

{|align="center"
|-
|[[Image:JyxNH3_NBO_1.jpg|thumb|200px|left|NBO analysis: charge number of NH3]]
|[[Image:NH3_NBO_2.jpg|thumb|200px|left|NBOanalysis: colour by charge of NH3]]

|}

===Frequency Analysis===

Log file for this calculation can be viewed here:https://wiki.ch.ic.ac.uk/wiki/images/7/79/JYX_NH3_FREQ.LOG

{| class="wikitable" border="1"
|+ ''Table.11'' Vibrational Frequencies of NH3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:NH3_freq_v1.jpg|right]]||||align="center"| 519 ||align="center"| 556.33 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:NH3_freq_v2.jpg|right]]||||align="center"| 1830 ||align="center"| 29.34 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:NH3_freq_v3.jpg|right]]|| ||align="center"| 1830 ||align="center"| 29.34 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:NH3_freq_v4.jpg|right]]|| ||align="center"| 3589 ||align="center"| 0.7 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:NH3_freq_v5.jpg|right]]|| ||align="center"| 3772||align="center"| 6.95 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:NH3_freq_v6.jpg|right]]|| ||align="center"| 3772||align="center"| 6.95 ||align="center"| E'
|}

[[Image:JyxIR.jpg]]

== '''References''' ==
<references />

Rep:Module2:JYX08

2011-02-08T16:58:50Z

Jyx08: /* Frequency Analysis */

=Part I: Small Molecule Optimisation=

==BH3==

===Optimisation===

BH3 is optimised using Gaussian, this was done using the B3LYP method with basis set of 3-21G. This is a rather "simple" basis set. It works well when it is applied to small molecules, when it is applied to large or complicated molecules will result in an inaccurate calculation. However, for this calculation for BH3, it is enough to obtain a good approximation. The molecule was drawn in Gaussview, and each BH bond was adjusted to 1.5Å first in prior of taking the optimisation to set ourselves a good starting point.

A summary of the optimisation is shown in the table below:

{| class="wikitable" border="1"
|+ ''Table. 1'' '''BH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3jyx.mol</uploadedFileContents>
<text>BH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|3-21G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -26.4622 a.u (-69.475 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|10.0 sec
|----
|B-H Bond length
|1.19Å
|----
|HBH Bond angle
|120.0°
|----
|}

The log file can be viewed here: https://www.ch.ic.ac.uk/wiki/images/4/46/BH3_OPTJYX.LOG

As we can see here, the optimised bond length is 1.19Å while the bond angle is 120.0°, which agrees well with the literature<ref name="j.jssc.2007.01.031"> M. R. Hartman, J. J. Rush, T. J. Udovic, R. C. Bowman Jr and S. J. Hwang ''J. Solid State. Chem.'', 2007, '''180''', 1298 - 1305 {{DOI|10.1016/j.jssc.2007.01.031}}</ref> experimental observations, which has proven that BH3 adopts a trigonal planar structure of bond length 1.21Å and bond angle 120.0°.

The RMS and Energy curves can be viewed after the run. The graphs represent the change in energy and RMS gradient against the calculation step. As the RMS gradient converges to 0, means that the total energy is minimised and the geometry of the molecule is therefore fully optimised.
[[Image:JyxBh3optgraph.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
We can see from the graph above, that it took 5 steps of calculation for the geometry of BH3 to be fully optimised, and the gradient has successfully converged to 0.

===Molecular Orbital Analysis===
The molecular orbital of BH3 was generated computationally. The result of this was then compared with the predicted molecular orbitals using linear combination of atomic orbitals (LCAO) method, and the two were found matches quite well. This indicates that the qualitative MO theory is quite accurate in terms of determining the shape of the MOs. However the downside is that it cannot predict the energies for the MOs quantitatively as the computational method.

The comparison of the MOs are shown below:

[[Image:Jyx BH3 MO.gif]]

The job was published in D-space: http://hdl.handle.net/10042/to-6885

=== NBO Analysis ===
{|align="right"
|-
|[[Image:BH3-NMO.jpg|thumb|200px|left|NBOanalysis: colour by charge of BH3]]

|}

The Natural Bond Orbital (NBO) analysis investigates the charge distribution in a molecule. From the log file, the overall charge is zero as we expect. All three of the H atoms have full s orbital contribution, where as for B atom, it has 33% contribution from the s, and 66% from the p orbitals. The colour appeared on the molecule corresponds to the charge distribution in this molecule. Bright green indicates highly positive charge and bright red highly negative charge. As expected the boron atom which is Lewis deficient is highly positively charged.

===Vibrational Analysis===
On the optimised BH3 molecule, a frequency analysis was performed:

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/3/33/JYX_BH3_FREQ.LOG
{| class="wikitable" border="1"
|+ ''Table. 2'' '''BH3 Vibration Frequencies & Modes'''
|'''Mode'''
|'''Vibration'''
|'''Description'''
|'''Freq/cm-1'''
|'''Intensity'''
|'''Symmetry (D3h)'''
|'''Literature Freq /cm-1<ref name="Schuurman">M.S. Schuurman, W.D. Allen, H.F. Schaefer III, ''J. Comput. Chem.'', 2005, '''26''', 1106: {{DOI|10.1002/jcc.20238}}</ref>'''
|----
|1
|[[Image:JYX_BH3_vib1.gif|centre]]
|'''Out of plane wagging''': All H move in direction of arrow while B moves in the opposite direction.
|1145.7
|92.7
|A2"
|1159
|----
|2
|[[Image:JYX_BH3_vib2.gif|centre]]
|'''In-plane Scissoring''': 2 H move in the scissors-like fashion while B and the third H moves downwards as one unit, away from the 2H's.
|1205
|12.4
|E'
|1204.7
|----
|3
|[[Image:JYX_BH3_vib3.gif|centre]]
|'''In-plane Rocking''': 2H and B rock concertedly in plane as one unit, while the third H swings in opposite direction with larger amplitude.
|1205
|12.4
|E'
|1204.7
|----
|4
|[[Image:JYX_BH3_vib4.gif|centre]]
|'''Symmetric Stretching''': All three H move away from B within the BH3 plane, while the central B remains still.
|2592.8
|0
|A1'
|NA
|----
|5
|[[Image:JYX_BH3_vib5.gif|centre]]
|'''Asymmetric stretching''': two H moves, one away from the B center, and the other one comes towards B wagging in the plane of the molecule, while the third H remains still.
|2731.3
|103.8
|E'
|2616
|----
|6
|[[Image:JYX_BH3_vib6_1.gif|centre]]
|'''Asymmetric stretching''': two H move away (or toward) B in concerted motion, while third H moves towards (or in -- opposite to the two H), all in the plane of screen. B moves towards and away from this third H.
|2731.3
|103.8
|E'
|2616
|----
|}

After the vibrational frequency analysis was done, a predicted vibrational spectrum can be viewed.
[[Image:Jyx_BH3_IRspectrum.jpg|none|frame|Predicted IR Spectrum of BH3]]

From the vibrational frequency analysis, 6 vibrational modes were identified. However from the graph above, only 5 peaks can be oberved. This is due to the vibrational spectrum is highly dependent on the symmetry hence the dipole moments of the vibration modes. Therefore for symmetric vibrations, i.e. for vibration 4, due to the overall dipole moment is cancelled out by individual stretches, hence it does not appear on the IR spectrum.

==TlBr3==
===Optimisation===

The structure of TlBr3 was optimised again by Gaussian, the method we employed this time was slightly different from the one we used to carry out the optimisation for BH3. We have used a higher level of basis set (LanL2DZ) due to the heavier atoms being present.

Log file for the optimisation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/a/ab/Jyx_TLBR3_OPTIMISATION.LOG

{| class="wikitable" border="1"
|+ ''Table.3'' '''TlBr3 Optimisation''' <jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Tlbr3.mol</uploadedFileContents>
<text>TlBr3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|LANL2DZ
|----
|Charge
|0
|----
|Spin
|single
|----
|E(RB+HF-LYP)
| - 91.2181 a.u (-239.264 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|34.0 sec
|----
|Tl-Br bond length
|2.58Å
|----
|Br-Tl-Br angle
|120.0°
|----
|}
Bond length reported in literature<ref name="TBr3">J. Glaser, ''Acta Chem. Scand. A'', 1979, '''33''', 789</ref> is 2.52Å and bond angle is 120.0Å, which agrees well with calculated values obtained, the bond angle in our model also obeys the ideal geometry of a trigonal planar compound. Slight deviations could be accounted for, that the simulated conditions done by Gaussian are different from the conditions of measurement done experimentally.

[[Image:Jyx_RMS-gradient-total-energy-graph-tlbr3.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
From the graph above, we can see that the gradient has successfully converged to 0, and the total energy is also minimised, which corresponds to the most stable geometry of the molecule.

===Vibrational Analysis===

The log file can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/e/e3/Jyx_TLBR3_FREQUENCY.LOG
Vibration frequency analysis was done using the same method and basis set as we used to optimise the structure. This is essential as to ensure the results maintaining accuracy and consistency.

*Low frequencies reported in the log file for this calculations are: -3.4226 -0.0026 -0.0004 0.0015 3.9361 3.9361
*Real low frequencies actually start at: 46.4288 46.4291 52.1449

{| class="wikitable" border="1"
|+ ''Table.4'' Vibrational Frequencies of TlBr3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:Jyxtlbr3v1.png|right]]||'''In-Plane Scissoring''': 2 Br atoms move towards and away from each other in a in-phase motion, the other Br atom and the Tl atom move away from the scissor in the TlBr3 plane at a smaller amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:Jyxtlbr3v2.png|right]]||'''In-Plane Rocking''': 2 Br atoms and the Tl atom rock in the TlBr3 plane in a in-phase motion with the Tl not being completely stationary, while the Br atom at the top swings at a larger amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:Jyxtlbr3v3.png|right]]||'''Out-of-Plane Wagging''': All 3 Br atoms move together in a in-phase motion in and out of the TlBr3 plane , the Tl atom wagging out of phase at a smaller amplitude ||align="center"| 52.1 ||align="center"| 5.8 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:Jyxtlbr3v4.png|right]]||'''Symmetric Stretching''': the Tl atom remains stationary, while the Br atoms move towards and away from the Tl atom in the TlBr3 plane in a in-phase motion, ||align="center"| 165.3 ||align="center"| 0 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:Jyxtlbr3v5.png|right]]||'''Asymmetric Stretching''': the top Br atom remains stationary, while the other 2 Br atoms move towards and away from the Tl atom in the TlBr3 plane in a out-of-phase motion, and the Tl atom wags between the two atoms at a small amplitude. ||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:Jyxtlbr3v6.png|right]]||'''Asymmetric Stretching''': the top Br atoms oscillates out-of-phase with the other 2 Br atoms, towards and away from the Tl atom in the TlBr3 plane, while the Tl move towards and away from the top Br atom in concerted motion .||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|}

[[Image:JYX_TlBr3_-_IR_spec.jpg|centre]]

For symmetrical molecules, 3N-6 vibrational modes should be present, where N is the number of atoms. For non-symmetrical molecule, 3N-5 vibrational modes should be seen. Therefore, for both BH3 and TlBr3 symmetrical compounds, 6 vibrational modes should be observed, corresponding to Gaussian calculated results. However from the spectrum, only 3 peaks can be observed. This is due to two of the peaks corresponds to degenerate vibration motions, and there is also a symmetric vibration mode which will not be observed from the spectrum.

====Why Do a Frequency Analysis?====

In the optimisation step, the derivative of the total energy curve has reached zero. However this does not indicate whether it is a maximum or a minimum turning point. The frequency analysis is essentially the second derivative of the curve. It is important that all values we obtained need to be positive in order to confirm that it is a minimum turning point. Any negative values would indicate maximum turning point being present, and thus optimisation has failed.

====Missing Bonds in Guassview====

Some molecules after being optimised by Gaussian, some of the bonds have disappeared. This doesn't not mean that there is no bonds between the atoms, it simply means that the bond length has exceeded the limit that was originally set for Gaussview. Thus Gaussview does not recognise this as a bonding interaction, hence does not draw the bonds in, but there are certainly bonding interactions present.

====Definition of a Bond====

A bond would be regard as a force of attraction between two or more atoms which stabilise the energy of the system. Sufficient overlap of orbitals of at least two atoms would result in formation of a bond. Bonding can also be described as a result of electromagnetic interaction between positively charged nuclei and negatively charged shared electrons (covalent bond), electrostatic interaction due to large difference in electronegativity(ionic bond).

=Part II: An Organometallic Complex=

==Mo(CO)4(PCl3)2 Cis-Trans Isomerism==

===Optimisation===
The cis and trans isomers of Mo(CO)4(PCl3)2 are optimised by the method B3LYP in Gaussian. They were pre-optimised using the pseudo potential/basis set of LanL2MB to get close to the structure with the minimal energy (opt=loose), and subsequently optimised a second time while manually rotated the bonds to force the molecule in a geometry close to the low energy conformation, with the pseudo potential being LanL2DZ. Pseudo potentials are applied here to provide a higher level of optimisation for these heavier atoms. LanL2DZ is an even higher level optimisation than LanL2MB, more suited to this large complex with heavy atoms like Mo.

{| class="wikitable" border="1"
|+ ''Table.5'' '''Mo(CO)4(PCl3)2 Optimisation'''
|'''''(1st optimisation)'''''
|
|
|----
|
|'''cis-isomer'''
|'''trans-isomer'''
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-rough.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx-Stagg-trans-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6894}}
|{{DOI|10042/to-6893}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2MB
|LANL2MB
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| - 617.5252 au (-1637.923 kJ/mol)
| - 617.5221 au (-1637.915 kJ/mol)
|----
|Dipole Moment
|8.42 Debye
|0.00 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|10min 56sec
|03min 07sec
|----
|'''''(2nd optimisation)'''''
|
|
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-modified.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Trans-eclips-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6895}}
|{{DOI|10042/to-6896}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2DZ
|LANL2DZ
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| -623.5771 a.u. (-1653.976 kJ/mol)
| -623.5760 a.u. (-1653.973 kJ/mol)
|----
|Dipole Moment
|1.31 Debye
|0.31 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|18min 38sec
|11min 38sec
|----
|}

Looking solely at the second optimisation, the energy of the cis isomer is ~3Jmol-1 higher than for the trans isomer, which means that the trans isomer is a thermodynamically favoured structure in relative to the cis isomer. This effect can be rationalised in terms of the steric effects. The PCl3 group can be considered relatively bulky and spatially demanding. The molecule will be in its low energy state when two groups are kept as far apart as possible in a trans geometry. This theory was in fact backed up by the experimental observation reported in a literature paper <ref name="Mo_trans">D. J. Darensbourg, ''Inorg. Chem.'', 1979, '''18''', 14. {{DOI|10.1021/ic50191a003}}</ref>. However the trans-isomer is no longer perfectly symmetric after the second optimisation. The bond angle between the two trans P groups has shifted from 180° to 177.4°, which the molecule results in having a very slight dipole moment of 0.31 Debye. The Mo-C bond has a distance of 2.06 Å and Mo-P with a distance of 2.44 Angstroms(corresponding well with 2.5Å in literature <ref>Structural characterizations of cis-Mo(CO)4(PPhMe2)(NHC5H10) and cis-Mo(CO)4(PPhMe2)(PPh3) and their solution reactivities toward carbon monoxide F. Albert. Cotton, Donald J. Darensbourg, Simonetta. Klein, Brian W. S. Kolthammer, Inorg. Chem., 1982, 21 (4), pp 1651–1655. Inorganica Chimica Acta, Volume 254, Issue 1, 1 January 1997, Pages 167-171, Crystal structures of trans-[Mo(CO)4(PPh3)2] and 1,4-bis (diphenylphosphino)-2,5-difluorobenzene, Graeme Hogarth and Tim Norman</ref>). In the case of cis-isomer, Mo-C bond length is about 2.06Å and Mo-P is ~2.51Å .

''Table.6'' Geometry data of trans-isomer compared to literature values
{| width="70%" border="1"
|-
| align="center" |
| align="center" |lit.<ref name="translit">D. W. Bennett, T. A. Siddiquee, D. T. Haworth, S. E. Kabir, F. K. Camellia, ''J. Chem. Crys.'', '''2004''', ''34'', 353-359.{{DOI|10.1023/B:JOCC.0000028667.12964.28}}</ref> trans [Cr(CO)4(PPh3)2]
| align="center" | trans [Mo(CO)4(PCl3)2]
|-
| align="left" | mean Mo-P bond length / Å
| align="center" | 2.36
| align="center" | 2.44
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 1.87
| align="center" | 2.06
|-
| align="left" | P-Mo-P bond angle/ °
| align="center" | 176.7
| align="center" | 177.4
|-
| align="left" | P-Mo-C bond angle / °
| align="center" | 89.5
| align="center" | 90(averaged)
|}
''Table.7'' Geometry data of cis-isomer compared to literature value
{| width="70%" border="1"
|-
| align="left" |
| align="center" |lit.<ref name="cislit">D. J. Darensbourg, R. L. Kump, ''Inorg. Chem.'', '''1978''', ''17'', 2680-2682. {{DOI|10.1021/ic50187a062}}</ref> cis [Mo(CO)4(PPh3)2]
| align="center" | cis [Mo(CO)4(PCl3)2]
|-
| align="left" | mean P-Mo bond length / Å
| align="center" | 2.51
| align="center" | 2.48
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 2.03
| align="center" | 2.03
|-
| align="left" | P-Mo-P bond angle / °
| align="center" | 94.2
| align="center" | 95.6
|-
| align="left" | P-Mo-C (trans to P) bond angle / °
| align="center" | 176.1
| align="center" | 174.4
|-
| align="left" | P-Mo-C (cis to P) bond angle/ °
| align="center" | 90.1
| align="center" | 87.3
|}

From the table above, the calculated data values agrees well with the literature.

===Frequency/IR analysis===

Trans frequency output file on D-space: |{{DOI|10042/to-6942}}
Cis frequency output on D-space: |{{DOI|10042/to-6941}}

All the low frequencies are positive which indicates that both molecule are at the energy minima, and the geometry is successfully optimised.

The low frequencies vibrations of both Mo(CO)4(PCl3)2 isomers are shown below:

{| class="wikitable" border="1"
|+ '''Table.8''' Low frequencies vibrations of both Mo(CO)4(PCl3)2 Isomers
! Isomer !!width="400"| Form of Vibration !! Frequency / cm-1 !! Intensity !! Symmetry (C1 Point Group)
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v1.jpg|150px|center]]||align="center"| 4.98 ||align="center"| 0.01 ||align="center"| A
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v2.jpg|150px|center]]||align="center"| 6.13 ||align="center"| 0.00 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v1.jpg|150px|center]] ||align="center"| 10.73 ||align="center"| 0.0264 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v2.jpg|150px|center]] ||align="center"| 17.62 ||align="center"| 0.0074 ||align="center"| A
|}

The carbonyl stretch vibrations are shifted about 40-50 cm-1, this is because the triphophine groups used in the experimental measurement are now replaced by PCl3 for this calculation. Due to symmetry of the vibrations for the trans-isomer, there are 2 IR inactive modes which does not appear on the spectrum.
{| class="wikitable" border="1"
|+ '''Table.9''' Carbonyl Stretching Frequencies of Mo(CO)4(PCl3)2''
! Isomer !! Calculated Frequency / cm-1 !! Calculated Intensity !! Experimental Frequency !! Point Group (C2v Symmetry)<ref name="Cotton">F.A. Cotton, ''Inorg. Chem.'', 1964, '''3''', 702: {{DOI|10.1021/ic50015a024}}</ref>
|-
|align="center"| cis ||align="center"| 1945.3 ||align="center"| 762.7 ||align="center"| 1986 ||align="center"| B2
|-
|align="center"| cis ||align="center"| 1948.7 ||align="center"| 1948.5 ||align="center"| 1994||align="center"| B1
|-
|align="center"| cis ||align="center"| 1958.3 ||align="center"| 633.0 ||align="center"| 2004 ||align="center"| A1
|-
|align="center"| cis ||align="center"| 2023.3 ||align="center"| 597.5 ||align="center"| 2072 ||align="center"| A1
|-
|align="center"| trans ||align="center"| 1950.5 ||align="center"| 1475.4 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1951.1 ||align="center"| 1466.7 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1977.4 ||align="center"| 0.63 ||align="center"| - ||align="center"| B1g
|-
|align="center"| trans ||align="center"| 2031.1 ||align="center"| 3.8 ||align="center"| - ||align="center"| A1g
|}

{| align="center" width="100%" border="0"
|-
| align="center" |[[Image:Trans-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of trans-isomer]]
| align="center" |[[Image:Cis-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of cis-isomer]]
|}

All four CO vibrations were observed in the spectrum for the cis-isomer, while only one peak was obersved for the trans-isomer due to the degenerate vibration states, thus only one CO stretch peak was seen for the IR spectrum of the trans-isomer.

=Part III: Mini-Project=

==NH3==
===Optimisation===

{| class="wikitable" border="1"
|+ ''Table. 10'' '''NH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>JyxNH3_OPT.mol</uploadedFileContents>
<text>NH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|6-31G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -56.531 a.u (-43.402 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|C3
|----
|Job cpu time
|12.0 sec
|----
|B-H Bond length
|1.006Å
|----
|HBH Bond angle
|116.251°
|----
|}

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/f/fa/JyxNH3_OPT.LOG‎
[[Image:JyxNH3_optimisation_graph.jpg]]

===MO Analysis===
Log file for this calculation can be viewed here:{{DOI|10042/to-7047}}
{| {{table}} border="1" style="text-align:center; border:1px solid black;"
| align="center" style="background:#f0f0f0;"|'''Orbital'''
| align="center" style="background:#f0f0f0;"|'''MO of NH3'''
| align="center" style="background:#f0f0f0;"|'''MO of BH3'''
|-
| A1'||[[Image:Jyx-NH3_MO2.jpg|200px]]||[[Image:SJCryer_MO_2.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO4.jpg|200px]]||[[Image:SJCryer_MO_3.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO3.jpg|200px]]||[[Image:SJCryer_MO_4.jpg|230px]]
|-
| A2<nowiki>"</nowiki>||[[Image:Jyx-NH3_MO5.jpg|200px]]||[[Image:SJCryer_MO_5.jpg|230px]]
|-
| A1'||[[Image:Jyx-NH3_MO6.jpg|200px]]||[[Image:SJCryer_MO_6.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO7.jpg|200px]]||[[Image:SJCryer_MO_7.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO8.jpg|200px]]||[[Image:SJCryer_MO_8.jpg|230px]]
|}

{|align="center"
|-
|[[Image:JyxNH3_NBO_1.jpg|thumb|200px|left|NBO analysis: charge number of NH3]]
|[[Image:NH3_NBO_2.jpg|thumb|200px|left|NBOanalysis: colour by charge of NH3]]

|}

===Frequency Analysis===

Log file for this calculation can be viewed here:https://wiki.ch.ic.ac.uk/wiki/images/7/79/JYX_NH3_FREQ.LOG

{| class="wikitable" border="1"
|+ ''Table.11'' Vibrational Frequencies of NH3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:NH3_freq_v1.jpg|right]]||||align="center"| 519 ||align="center"| 556.33 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:NH3_freq_v2.jpg|right]]||||align="center"| 1830 ||align="center"| 29.34 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:NH3_freq_v3.jpg|right]]|| ||align="center"| 1830 ||align="center"| 29.34 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:NH3_freq_v4.jpg|right]]|| ||align="center"| 3589 ||align="center"| 0.7 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:NH3_freq_v5.jpg|right]]|| ||align="center"| 3772||align="center"| 6.95 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:NH3_freq_v6.jpg|right]]|| ||align="center"| 3772||align="center"| 6.95 ||align="center"| E'
|}

Image:JyxIR.jpg[[Image:Image:JyxIR.jpg]]

== '''References''' ==
<references />

File:JyxIR.jpg

2011-02-08T16:58:26Z

Jyx08:

Rep:Module2:JYX08

2011-02-08T16:56:12Z

Jyx08: /* Frequency Analysis */

Rep:Module2:JYX08

2011-02-08T16:53:10Z

Jyx08: /* Frequency Analysis */

=Part I: Small Molecule Optimisation=

==BH3==

===Optimisation===

BH3 is optimised using Gaussian, this was done using the B3LYP method with basis set of 3-21G. This is a rather "simple" basis set. It works well when it is applied to small molecules, when it is applied to large or complicated molecules will result in an inaccurate calculation. However, for this calculation for BH3, it is enough to obtain a good approximation. The molecule was drawn in Gaussview, and each BH bond was adjusted to 1.5Å first in prior of taking the optimisation to set ourselves a good starting point.

A summary of the optimisation is shown in the table below:

{| class="wikitable" border="1"
|+ ''Table. 1'' '''BH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>BH3jyx.mol</uploadedFileContents>
<text>BH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|3-21G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -26.4622 a.u (-69.475 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|10.0 sec
|----
|B-H Bond length
|1.19Å
|----
|HBH Bond angle
|120.0°
|----
|}

The log file can be viewed here: https://www.ch.ic.ac.uk/wiki/images/4/46/BH3_OPTJYX.LOG

As we can see here, the optimised bond length is 1.19Å while the bond angle is 120.0°, which agrees well with the literature<ref name="j.jssc.2007.01.031"> M. R. Hartman, J. J. Rush, T. J. Udovic, R. C. Bowman Jr and S. J. Hwang ''J. Solid State. Chem.'', 2007, '''180''', 1298 - 1305 {{DOI|10.1016/j.jssc.2007.01.031}}</ref> experimental observations, which has proven that BH3 adopts a trigonal planar structure of bond length 1.21Å and bond angle 120.0°.

The RMS and Energy curves can be viewed after the run. The graphs represent the change in energy and RMS gradient against the calculation step. As the RMS gradient converges to 0, means that the total energy is minimised and the geometry of the molecule is therefore fully optimised.
[[Image:JyxBh3optgraph.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
We can see from the graph above, that it took 5 steps of calculation for the geometry of BH3 to be fully optimised, and the gradient has successfully converged to 0.

===Molecular Orbital Analysis===
The molecular orbital of BH3 was generated computationally. The result of this was then compared with the predicted molecular orbitals using linear combination of atomic orbitals (LCAO) method, and the two were found matches quite well. This indicates that the qualitative MO theory is quite accurate in terms of determining the shape of the MOs. However the downside is that it cannot predict the energies for the MOs quantitatively as the computational method.

The comparison of the MOs are shown below:

[[Image:Jyx BH3 MO.gif]]

The job was published in D-space: http://hdl.handle.net/10042/to-6885

=== NBO Analysis ===
{|align="right"
|-
|[[Image:BH3-NMO.jpg|thumb|200px|left|NBOanalysis: colour by charge of BH3]]

|}

The Natural Bond Orbital (NBO) analysis investigates the charge distribution in a molecule. From the log file, the overall charge is zero as we expect. All three of the H atoms have full s orbital contribution, where as for B atom, it has 33% contribution from the s, and 66% from the p orbitals. The colour appeared on the molecule corresponds to the charge distribution in this molecule. Bright green indicates highly positive charge and bright red highly negative charge. As expected the boron atom which is Lewis deficient is highly positively charged.

===Vibrational Analysis===
On the optimised BH3 molecule, a frequency analysis was performed:

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/3/33/JYX_BH3_FREQ.LOG
{| class="wikitable" border="1"
|+ ''Table. 2'' '''BH3 Vibration Frequencies & Modes'''
|'''Mode'''
|'''Vibration'''
|'''Description'''
|'''Freq/cm-1'''
|'''Intensity'''
|'''Symmetry (D3h)'''
|'''Literature Freq /cm-1<ref name="Schuurman">M.S. Schuurman, W.D. Allen, H.F. Schaefer III, ''J. Comput. Chem.'', 2005, '''26''', 1106: {{DOI|10.1002/jcc.20238}}</ref>'''
|----
|1
|[[Image:JYX_BH3_vib1.gif|centre]]
|'''Out of plane wagging''': All H move in direction of arrow while B moves in the opposite direction.
|1145.7
|92.7
|A2"
|1159
|----
|2
|[[Image:JYX_BH3_vib2.gif|centre]]
|'''In-plane Scissoring''': 2 H move in the scissors-like fashion while B and the third H moves downwards as one unit, away from the 2H's.
|1205
|12.4
|E'
|1204.7
|----
|3
|[[Image:JYX_BH3_vib3.gif|centre]]
|'''In-plane Rocking''': 2H and B rock concertedly in plane as one unit, while the third H swings in opposite direction with larger amplitude.
|1205
|12.4
|E'
|1204.7
|----
|4
|[[Image:JYX_BH3_vib4.gif|centre]]
|'''Symmetric Stretching''': All three H move away from B within the BH3 plane, while the central B remains still.
|2592.8
|0
|A1'
|NA
|----
|5
|[[Image:JYX_BH3_vib5.gif|centre]]
|'''Asymmetric stretching''': two H moves, one away from the B center, and the other one comes towards B wagging in the plane of the molecule, while the third H remains still.
|2731.3
|103.8
|E'
|2616
|----
|6
|[[Image:JYX_BH3_vib6_1.gif|centre]]
|'''Asymmetric stretching''': two H move away (or toward) B in concerted motion, while third H moves towards (or in -- opposite to the two H), all in the plane of screen. B moves towards and away from this third H.
|2731.3
|103.8
|E'
|2616
|----
|}

After the vibrational frequency analysis was done, a predicted vibrational spectrum can be viewed.
[[Image:Jyx_BH3_IRspectrum.jpg|none|frame|Predicted IR Spectrum of BH3]]

From the vibrational frequency analysis, 6 vibrational modes were identified. However from the graph above, only 5 peaks can be oberved. This is due to the vibrational spectrum is highly dependent on the symmetry hence the dipole moments of the vibration modes. Therefore for symmetric vibrations, i.e. for vibration 4, due to the overall dipole moment is cancelled out by individual stretches, hence it does not appear on the IR spectrum.

==TlBr3==
===Optimisation===

The structure of TlBr3 was optimised again by Gaussian, the method we employed this time was slightly different from the one we used to carry out the optimisation for BH3. We have used a higher level of basis set (LanL2DZ) due to the heavier atoms being present.

Log file for the optimisation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/a/ab/Jyx_TLBR3_OPTIMISATION.LOG

{| class="wikitable" border="1"
|+ ''Table.3'' '''TlBr3 Optimisation''' <jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Tlbr3.mol</uploadedFileContents>
<text>TlBr3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|LANL2DZ
|----
|Charge
|0
|----
|Spin
|single
|----
|E(RB+HF-LYP)
| - 91.2181 a.u (-239.264 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|D3h
|----
|Job cpu time
|34.0 sec
|----
|Tl-Br bond length
|2.58Å
|----
|Br-Tl-Br angle
|120.0°
|----
|}
Bond length reported in literature<ref name="TBr3">J. Glaser, ''Acta Chem. Scand. A'', 1979, '''33''', 789</ref> is 2.52Å and bond angle is 120.0Å, which agrees well with calculated values obtained, the bond angle in our model also obeys the ideal geometry of a trigonal planar compound. Slight deviations could be accounted for, that the simulated conditions done by Gaussian are different from the conditions of measurement done experimentally.

[[Image:Jyx_RMS-gradient-total-energy-graph-tlbr3.jpg|none|frame|RMS Gradient and Total Energy Graphs]]
From the graph above, we can see that the gradient has successfully converged to 0, and the total energy is also minimised, which corresponds to the most stable geometry of the molecule.

===Vibrational Analysis===

The log file can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/e/e3/Jyx_TLBR3_FREQUENCY.LOG
Vibration frequency analysis was done using the same method and basis set as we used to optimise the structure. This is essential as to ensure the results maintaining accuracy and consistency.

*Low frequencies reported in the log file for this calculations are: -3.4226 -0.0026 -0.0004 0.0015 3.9361 3.9361
*Real low frequencies actually start at: 46.4288 46.4291 52.1449

{| class="wikitable" border="1"
|+ ''Table.4'' Vibrational Frequencies of TlBr3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:Jyxtlbr3v1.png|right]]||'''In-Plane Scissoring''': 2 Br atoms move towards and away from each other in a in-phase motion, the other Br atom and the Tl atom move away from the scissor in the TlBr3 plane at a smaller amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:Jyxtlbr3v2.png|right]]||'''In-Plane Rocking''': 2 Br atoms and the Tl atom rock in the TlBr3 plane in a in-phase motion with the Tl not being completely stationary, while the Br atom at the top swings at a larger amplitude ||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:Jyxtlbr3v3.png|right]]||'''Out-of-Plane Wagging''': All 3 Br atoms move together in a in-phase motion in and out of the TlBr3 plane , the Tl atom wagging out of phase at a smaller amplitude ||align="center"| 52.1 ||align="center"| 5.8 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:Jyxtlbr3v4.png|right]]||'''Symmetric Stretching''': the Tl atom remains stationary, while the Br atoms move towards and away from the Tl atom in the TlBr3 plane in a in-phase motion, ||align="center"| 165.3 ||align="center"| 0 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:Jyxtlbr3v5.png|right]]||'''Asymmetric Stretching''': the top Br atom remains stationary, while the other 2 Br atoms move towards and away from the Tl atom in the TlBr3 plane in a out-of-phase motion, and the Tl atom wags between the two atoms at a small amplitude. ||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:Jyxtlbr3v6.png|right]]||'''Asymmetric Stretching''': the top Br atoms oscillates out-of-phase with the other 2 Br atoms, towards and away from the Tl atom in the TlBr3 plane, while the Tl move towards and away from the top Br atom in concerted motion .||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|}

[[Image:JYX_TlBr3_-_IR_spec.jpg|centre]]

For symmetrical molecules, 3N-6 vibrational modes should be present, where N is the number of atoms. For non-symmetrical molecule, 3N-5 vibrational modes should be seen. Therefore, for both BH3 and TlBr3 symmetrical compounds, 6 vibrational modes should be observed, corresponding to Gaussian calculated results. However from the spectrum, only 3 peaks can be observed. This is due to two of the peaks corresponds to degenerate vibration motions, and there is also a symmetric vibration mode which will not be observed from the spectrum.

====Why Do a Frequency Analysis?====

In the optimisation step, the derivative of the total energy curve has reached zero. However this does not indicate whether it is a maximum or a minimum turning point. The frequency analysis is essentially the second derivative of the curve. It is important that all values we obtained need to be positive in order to confirm that it is a minimum turning point. Any negative values would indicate maximum turning point being present, and thus optimisation has failed.

====Missing Bonds in Guassview====

Some molecules after being optimised by Gaussian, some of the bonds have disappeared. This doesn't not mean that there is no bonds between the atoms, it simply means that the bond length has exceeded the limit that was originally set for Gaussview. Thus Gaussview does not recognise this as a bonding interaction, hence does not draw the bonds in, but there are certainly bonding interactions present.

====Definition of a Bond====

A bond would be regard as a force of attraction between two or more atoms which stabilise the energy of the system. Sufficient overlap of orbitals of at least two atoms would result in formation of a bond. Bonding can also be described as a result of electromagnetic interaction between positively charged nuclei and negatively charged shared electrons (covalent bond), electrostatic interaction due to large difference in electronegativity(ionic bond).

=Part II: An Organometallic Complex=

==Mo(CO)4(PCl3)2 Cis-Trans Isomerism==

===Optimisation===
The cis and trans isomers of Mo(CO)4(PCl3)2 are optimised by the method B3LYP in Gaussian. They were pre-optimised using the pseudo potential/basis set of LanL2MB to get close to the structure with the minimal energy (opt=loose), and subsequently optimised a second time while manually rotated the bonds to force the molecule in a geometry close to the low energy conformation, with the pseudo potential being LanL2DZ. Pseudo potentials are applied here to provide a higher level of optimisation for these heavier atoms. LanL2DZ is an even higher level optimisation than LanL2MB, more suited to this large complex with heavy atoms like Mo.

{| class="wikitable" border="1"
|+ ''Table.5'' '''Mo(CO)4(PCl3)2 Optimisation'''
|'''''(1st optimisation)'''''
|
|
|----
|
|'''cis-isomer'''
|'''trans-isomer'''
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-rough.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx-Stagg-trans-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6894}}
|{{DOI|10042/to-6893}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2MB
|LANL2MB
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| - 617.5252 au (-1637.923 kJ/mol)
| - 617.5221 au (-1637.915 kJ/mol)
|----
|Dipole Moment
|8.42 Debye
|0.00 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|10min 56sec
|03min 07sec
|----
|'''''(2nd optimisation)'''''
|
|
|----
|Jmol
|<jmol>
<jmolAppletButton>
<uploadedFileContents>JyxCis-Mo-modified.mol</uploadedFileContents>
<text>Cis isomer</text>
</jmolAppletButton>
</jmol>
|<jmol>
<jmolAppletButton>
<uploadedFileContents>Jyx_Trans-eclips-Mo.mol</uploadedFileContents>
<text>Trans isomer</text>
</jmolAppletButton>
</jmol>
|----
|D-space link
|{{DOI|10042/to-6895}}
|{{DOI|10042/to-6896}}
|----
|File Type
|.fch
|.fch
|----
|Calculation type
|FOPT
|FOPT
|----
|Calculation method
|RB3LYP
|RB3LYP
|----
|Basis set
|LANL2DZ
|LANL2DZ
|----
|Charge
|0
|0
|----
|Spin
|singlet
|singlet
|----
|E(RB+HF-LYP)
| -623.5771 a.u. (-1653.976 kJ/mol)
| -623.5760 a.u. (-1653.973 kJ/mol)
|----
|Dipole Moment
|1.31 Debye
|0.31 Debye
|----
|Point Group
|C1
|C1
|----
|Job cpu time
|18min 38sec
|11min 38sec
|----
|}

Looking solely at the second optimisation, the energy of the cis isomer is ~3Jmol-1 higher than for the trans isomer, which means that the trans isomer is a thermodynamically favoured structure in relative to the cis isomer. This effect can be rationalised in terms of the steric effects. The PCl3 group can be considered relatively bulky and spatially demanding. The molecule will be in its low energy state when two groups are kept as far apart as possible in a trans geometry. This theory was in fact backed up by the experimental observation reported in a literature paper <ref name="Mo_trans">D. J. Darensbourg, ''Inorg. Chem.'', 1979, '''18''', 14. {{DOI|10.1021/ic50191a003}}</ref>. However the trans-isomer is no longer perfectly symmetric after the second optimisation. The bond angle between the two trans P groups has shifted from 180° to 177.4°, which the molecule results in having a very slight dipole moment of 0.31 Debye. The Mo-C bond has a distance of 2.06 Å and Mo-P with a distance of 2.44 Angstroms(corresponding well with 2.5Å in literature <ref>Structural characterizations of cis-Mo(CO)4(PPhMe2)(NHC5H10) and cis-Mo(CO)4(PPhMe2)(PPh3) and their solution reactivities toward carbon monoxide F. Albert. Cotton, Donald J. Darensbourg, Simonetta. Klein, Brian W. S. Kolthammer, Inorg. Chem., 1982, 21 (4), pp 1651–1655. Inorganica Chimica Acta, Volume 254, Issue 1, 1 January 1997, Pages 167-171, Crystal structures of trans-[Mo(CO)4(PPh3)2] and 1,4-bis (diphenylphosphino)-2,5-difluorobenzene, Graeme Hogarth and Tim Norman</ref>). In the case of cis-isomer, Mo-C bond length is about 2.06Å and Mo-P is ~2.51Å .

''Table.6'' Geometry data of trans-isomer compared to literature values
{| width="70%" border="1"
|-
| align="center" |
| align="center" |lit.<ref name="translit">D. W. Bennett, T. A. Siddiquee, D. T. Haworth, S. E. Kabir, F. K. Camellia, ''J. Chem. Crys.'', '''2004''', ''34'', 353-359.{{DOI|10.1023/B:JOCC.0000028667.12964.28}}</ref> trans [Cr(CO)4(PPh3)2]
| align="center" | trans [Mo(CO)4(PCl3)2]
|-
| align="left" | mean Mo-P bond length / Å
| align="center" | 2.36
| align="center" | 2.44
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 1.87
| align="center" | 2.06
|-
| align="left" | P-Mo-P bond angle/ °
| align="center" | 176.7
| align="center" | 177.4
|-
| align="left" | P-Mo-C bond angle / °
| align="center" | 89.5
| align="center" | 90(averaged)
|}
''Table.7'' Geometry data of cis-isomer compared to literature value
{| width="70%" border="1"
|-
| align="left" |
| align="center" |lit.<ref name="cislit">D. J. Darensbourg, R. L. Kump, ''Inorg. Chem.'', '''1978''', ''17'', 2680-2682. {{DOI|10.1021/ic50187a062}}</ref> cis [Mo(CO)4(PPh3)2]
| align="center" | cis [Mo(CO)4(PCl3)2]
|-
| align="left" | mean P-Mo bond length / Å
| align="center" | 2.51
| align="center" | 2.48
|-
| align="left" | mean Mo-C bond length / Å
| align="center" | 2.03
| align="center" | 2.03
|-
| align="left" | P-Mo-P bond angle / °
| align="center" | 94.2
| align="center" | 95.6
|-
| align="left" | P-Mo-C (trans to P) bond angle / °
| align="center" | 176.1
| align="center" | 174.4
|-
| align="left" | P-Mo-C (cis to P) bond angle/ °
| align="center" | 90.1
| align="center" | 87.3
|}

From the table above, the calculated data values agrees well with the literature.

===Frequency/IR analysis===

Trans frequency output file on D-space: |{{DOI|10042/to-6942}}
Cis frequency output on D-space: |{{DOI|10042/to-6941}}

All the low frequencies are positive which indicates that both molecule are at the energy minima, and the geometry is successfully optimised.

The low frequencies vibrations of both Mo(CO)4(PCl3)2 isomers are shown below:

{| class="wikitable" border="1"
|+ '''Table.8''' Low frequencies vibrations of both Mo(CO)4(PCl3)2 Isomers
! Isomer !!width="400"| Form of Vibration !! Frequency / cm-1 !! Intensity !! Symmetry (C1 Point Group)
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v1.jpg|150px|center]]||align="center"| 4.98 ||align="center"| 0.01 ||align="center"| A
|-
|align="center"| ''trans''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-trans-mo-v2.jpg|150px|center]]||align="center"| 6.13 ||align="center"| 0.00 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v1.jpg|150px|center]] ||align="center"| 10.73 ||align="center"| 0.0264 ||align="center"| A
|-
|align="center"| ''cis''-Mo(CO)4(PCl3)2 ||[[Image:Jyx-cis-mo-v2.jpg|150px|center]] ||align="center"| 17.62 ||align="center"| 0.0074 ||align="center"| A
|}

The carbonyl stretch vibrations are shifted about 40-50 cm-1, this is because the triphophine groups used in the experimental measurement are now replaced by PCl3 for this calculation. Due to symmetry of the vibrations for the trans-isomer, there are 2 IR inactive modes which does not appear on the spectrum.
{| class="wikitable" border="1"
|+ '''Table.9''' Carbonyl Stretching Frequencies of Mo(CO)4(PCl3)2''
! Isomer !! Calculated Frequency / cm-1 !! Calculated Intensity !! Experimental Frequency !! Point Group (C2v Symmetry)<ref name="Cotton">F.A. Cotton, ''Inorg. Chem.'', 1964, '''3''', 702: {{DOI|10.1021/ic50015a024}}</ref>
|-
|align="center"| cis ||align="center"| 1945.3 ||align="center"| 762.7 ||align="center"| 1986 ||align="center"| B2
|-
|align="center"| cis ||align="center"| 1948.7 ||align="center"| 1948.5 ||align="center"| 1994||align="center"| B1
|-
|align="center"| cis ||align="center"| 1958.3 ||align="center"| 633.0 ||align="center"| 2004 ||align="center"| A1
|-
|align="center"| cis ||align="center"| 2023.3 ||align="center"| 597.5 ||align="center"| 2072 ||align="center"| A1
|-
|align="center"| trans ||align="center"| 1950.5 ||align="center"| 1475.4 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1951.1 ||align="center"| 1466.7 ||align="center"| 1896 ||align="center"| Eu
|-
|align="center"| trans ||align="center"| 1977.4 ||align="center"| 0.63 ||align="center"| - ||align="center"| B1g
|-
|align="center"| trans ||align="center"| 2031.1 ||align="center"| 3.8 ||align="center"| - ||align="center"| A1g
|}

{| align="center" width="100%" border="0"
|-
| align="center" |[[Image:Trans-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of trans-isomer]]
| align="center" |[[Image:Cis-mo-vib-spectrum.jpg|center|thumb|200px|IR spectrum of cis-isomer]]
|}

All four CO vibrations were observed in the spectrum for the cis-isomer, while only one peak was obersved for the trans-isomer due to the degenerate vibration states, thus only one CO stretch peak was seen for the IR spectrum of the trans-isomer.

=Part III: Mini-Project=

==NH3==
===Optimisation===

{| class="wikitable" border="1"
|+ ''Table. 10'' '''NH3 Optimisation Summary''' <jmol>
<jmolAppletButton>
<uploadedFileContents>JyxNH3_OPT.mol</uploadedFileContents>
<text>NH3</text>
</jmolAppletButton>
</jmol>
|File Type
|.log
|----
|Calculation type
|FOPT
|----
|Calculation method
|RB3LYP
|----
|Basis set
|6-31G
|----
|Charge
|0
|----
|Spin
|singlet
|----
|E(RB+HF-LYP)
| -56.531 a.u (-43.402 kJ/mol)
|----
|RMS Gradient Norm
|0.00 a.u.
|----
|Dipole Moment
|0.00 Debye
|----
|Point Group
|C3
|----
|Job cpu time
|12.0 sec
|----
|B-H Bond length
|1.006Å
|----
|HBH Bond angle
|116.251°
|----
|}

Log file for this calculation can be viewed here: https://wiki.ch.ic.ac.uk/wiki/images/f/fa/JyxNH3_OPT.LOG‎
[[Image:JyxNH3_optimisation_graph.jpg]]

===MO Analysis===
Log file for this calculation can be viewed here:{{DOI|10042/to-7047}}
{| {{table}} border="1" style="text-align:center; border:1px solid black;"
| align="center" style="background:#f0f0f0;"|'''Orbital'''
| align="center" style="background:#f0f0f0;"|'''MO of NH3'''
| align="center" style="background:#f0f0f0;"|'''MO of BH3'''
|-
| A1'||[[Image:Jyx-NH3_MO2.jpg|200px]]||[[Image:SJCryer_MO_2.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO4.jpg|200px]]||[[Image:SJCryer_MO_3.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO3.jpg|200px]]||[[Image:SJCryer_MO_4.jpg|230px]]
|-
| A2<nowiki>"</nowiki>||[[Image:Jyx-NH3_MO5.jpg|200px]]||[[Image:SJCryer_MO_5.jpg|230px]]
|-
| A1'||[[Image:Jyx-NH3_MO6.jpg|200px]]||[[Image:SJCryer_MO_6.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO7.jpg|200px]]||[[Image:SJCryer_MO_7.jpg|230px]]
|-
| E'||[[Image:Jyx-NH3_MO8.jpg|200px]]||[[Image:SJCryer_MO_8.jpg|230px]]
|}

{|align="center"
|-
|[[Image:JyxNH3_NBO_1.jpg|thumb|200px|left|NBO analysis: charge number of NH3]]
|[[Image:NH3_NBO_2.jpg|thumb|200px|left|NBOanalysis: colour by charge of NH3]]

|}

===Frequency Analysis===

Log file for this calculation can be viewed here:https://wiki.ch.ic.ac.uk/wiki/images/7/79/JYX_NH3_FREQ.LOG

{| class="wikitable" border="1"
|+ ''Table.11'' Vibrational Frequencies of NH3
! No. !!width="400"| Diagram !! Form of Vibration !! Calculated Frequency / cm-1 !! Intensity !! Symmetry (D3h Point Group)
|-
|align="center"| 1 ||align="center"|[[Image:NH3_freq_v1.jpg|right]]||||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 2 ||align="center"|[[Image:NH3_freq_v2.jpg|right]]||||align="center"| 46.4 ||align="center"| 3.7 ||align="center"| E'
|-
|align="center"| 3 ||align="center"|[[Image:NH3_freq_v3.jpg|right]]|| ||align="center"| 52.1 ||align="center"| 5.8 ||align="center"| A2'
|-
|align="center"| 4 ||align="center"|[[Image:NH3_freq_v4.jpg|right]]|| ||align="center"| 165.3 ||align="center"| 0 ||align="center"| A1'
|-
|align="center"| 5 ||align="center"|[[Image:NH3_freq_v5.jpg|right]]|| ||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|-
|align="center"| 6 ||align="center"|[[Image:NH3_freq_v6.jpg|right]]|| ||align="center"| 210.7 ||align="center"| 25.5 ||align="center"| E'
|}

== '''References''' ==
<references />