ChemWiki - User contributions [en]

Rep:Physical:luke4912

2009-11-13T16:47:35Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:XX1.jpg|300px|left]] [[Image:XX2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:XX3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:XX7.jpg|left]] [[Image:XX8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

[[Image:X10.jpg|200px|left]] [[Image:X11.jpg|250px|right]] A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|300px|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|thumb|centre|Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.]]

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|200px|left]][[Image:X18.jpg|200px|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:XX19.jpg|200px|left]][[Image:XX20.jpg|200px|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.JPG|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.JPG|thumb|Butadiene HOMO]]
| [[Image:X23.JPG|thumb|Butadiene LUMO]]
| [[Image:X24.JPG|thumb|Ethylene HOMO]]
| [[Image:X25.JPG|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T16:38:48Z

Lc407: /* Optimising the Chair Transition Structure */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:XX1.jpg|left]] [[Image:XX2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:XX3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:XX7.jpg|left]] [[Image:XX8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|thumb|centre|Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.]]

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.JPG|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.JPG|thumb|Butadiene HOMO]]
| [[Image:X23.JPG|thumb|Butadiene LUMO]]
| [[Image:X24.JPG|thumb|Ethylene HOMO]]
| [[Image:X25.JPG|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T16:36:46Z

Lc407: /* Transition State */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:XX1.jpg|left]] [[Image:XX2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:XX3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:XX7.jpg|left]] [[Image:XX8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.JPG|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.JPG|thumb|Butadiene HOMO]]
| [[Image:X23.JPG|thumb|Butadiene LUMO]]
| [[Image:X24.JPG|thumb|Ethylene HOMO]]
| [[Image:X25.JPG|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T16:36:27Z

Lc407: /* The Diels-Alder Cycloaddition */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:XX1.jpg|left]] [[Image:XX2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:XX3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:XX7.jpg|left]] [[Image:XX8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.JPG|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.JPG|thumb|Butadiene HOMO]]
| [[Image:X23.JPG|thumb|Butadiene LUMO]]
| [[Image:X24.JPG|thumb|Ethylene HOMO]]
| [[Image:X25.JPG|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.JPG|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T16:35:50Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:XX1.jpg|left]] [[Image:XX2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:XX3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:XX7.jpg|left]] [[Image:XX8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.jpg|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.jpg|thumb|Butadiene HOMO]]
| [[Image:X23.jpg|thumb|Butadiene LUMO]]
| [[Image:X24.jpg|thumb|Ethylene HOMO]]
| [[Image:X25.jpg|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

File:X28.jpg

2009-11-13T16:34:49Z

Lc407:

File:X27.jpg

2009-11-13T16:34:34Z

Lc407:

File:X26.jpg

2009-11-13T16:34:13Z

Lc407:

File:X25.JPG

2009-11-13T16:33:31Z

Lc407:

File:X24.JPG

2009-11-13T16:33:17Z

Lc407:

File:X23.JPG

2009-11-13T16:33:01Z

Lc407:

File:X22.JPG

2009-11-13T16:32:40Z

Lc407:

File:X21.JPG

2009-11-13T16:32:23Z

Lc407:

File:XX20.jpg

2009-11-13T16:31:47Z

Lc407:

File:XX19.jpg

2009-11-13T16:31:28Z

Lc407:

File:X19.jpg

2009-11-13T16:30:47Z

Lc407:

File:X18.jpg

2009-11-13T16:30:30Z

Lc407:

File:X17.jpg

2009-11-13T16:30:10Z

Lc407:

File:X16.jpg

2009-11-13T16:29:49Z

Lc407:

File:X14.jpg

2009-11-13T16:29:32Z

Lc407:

File:X13.jpg

2009-11-13T16:28:54Z

Lc407:

File:X12.jpg

2009-11-13T16:28:23Z

Lc407:

File:X11.jpg

2009-11-13T16:28:09Z

Lc407:

File:X10.jpg

2009-11-13T16:27:32Z

Lc407:

File:XX8.jpg

2009-11-13T16:27:06Z

Lc407:

File:XX7.jpg

2009-11-13T16:26:47Z

Lc407:

File:XX3.jpg

2009-11-13T16:26:25Z

Lc407:

File:XX2.jpg

2009-11-13T16:26:07Z

Lc407:

File:Lcanti1pic.jpg

2009-11-13T16:25:49Z

Lc407:

File:XX1.jpg

2009-11-13T16:25:32Z

Lc407:

Rep:Physical:luke4912

2009-11-13T16:23:29Z

Lc407: /* Transition State */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.jpg|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.jpg|thumb|Butadiene HOMO]]
| [[Image:X23.jpg|thumb|Butadiene LUMO]]
| [[Image:X24.jpg|thumb|Ethylene HOMO]]
| [[Image:X25.jpg|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical bond is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T16:22:35Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.jpg|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.jpg|thumb|Butadiene HOMO]]
| [[Image:X23.jpg|thumb|Butadiene LUMO]]
| [[Image:X24.jpg|thumb|Ethylene HOMO]]
| [[Image:X25.jpg|thumb|Ethylene LUMO]]
|}

===Transition State===
The transition state for this reaction can be thought of as an envelope structure - allowing π orbitals of both reactants to align and react. In this part of the module the transition structure was optimised using the same AM1 methodology (using frozen coordinates), as employed before. The optimisation structure is shown below, it yielded one imaginary frequency at -956 cm-1 suggesting the desired bonds had been formed.

[[Image:X26.jpg|centre]]

The HOMO and LUMO molecular orbitals were then plotted for the transition structure, these are shown below. It can be seen that the HOMO orbital is antisymmetric whilst the LUMO is symmetric. The reaction clearly works since the antisymmetric butadiene HOMO overlaps well with the antisymmetric ethylene LUMO to produce an antisymmetric transition structure.

{|
| [[Image:X27.jpg|thumb|Transition state HOMO]]
| [[Image:X28.jpg|thumb|Transition state LUMO]]
|}

Finally, by C-C bond length comparison it was deduced the transition structure was correct. The table below lists typical bond lengths for C-C bonds in the product cyclohexene, along with the C-C transition structure bond computed by Gaussian, and the VdW bond radius for comparison. What can be seen is the computed bond length is much longer than the ideal C-C bond in the product molecule suggesting the transition structure bonds are weaker and not fully formed. However, by being larger than the VdW value it signifies a chemical is present.

{| class="wikitable" border="1" align = center
|+ Cyclohexene bond lengths
! Bond !! Length/A !!
|-
| sp3 C-C || 1.55 ||
|-
| sp2 C=C|| 1.47 ||
|-
| Transition C-C (from Gaussian) || 2.19 ||
|-
| C VdW Radius || 1.70 ||
|}

Rep:Physical:luke4912

2009-11-13T14:55:09Z

Lc407: /* Molecular Orbitals */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.jpg|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.jpg|thumb|Butadiene HOMO]]
| [[Image:X23.jpg|thumb|Butadiene LUMO]]
| [[Image:X24.jpg|thumb|Ethylene HOMO]]
| [[Image:X25.jpg|thumb|Ethylene LUMO]]
|}

===Transition State===

The trasition state structure here can be thought of that in the diagram below. This allows the π orbitals of the ethylene to react with the π orbitals of the cis-butadiene. In the previous exercise, the guess distance between the fragments was 2.2 angstroms. This was the same as here.

The transition state was optimised with frequency calculation using the '''AM1 semi-empirical molecular orbital method'''. This calculation confirmed that the transition state structure here is the true one for the Diels Alder reaction being studied, due to the fact that the imaginary frequency here at -956 cm-1 corresponds to the forming of the desired bonds.

This frequency is illustrated below. It shows the bonds being formed in a '''synchronous''' fashion. This is different to the lowest possible real frequency 147 cm-1, which is asynchronous.

The HOMO (bottom) and LUMO (top) were then plotted. The HOMO here is antisymmetric, but the LUMO is symmetric.

The optimisation of the transition state above was carried out via calculating the force constants at the start of the calculation. It was also carried out using the redundant coordinate editor to allow comparison. A similar geometry, as expected, was formed:The trasition state structure here can be thought of that in the diagram below. This allows the π orbitals of the ethylene to react with the π orbitals of the cis-butadiene. In the previous exercise, the guess distance between the fragments was 2.2 angstroms. This was the same as here.

The transition state was optimised with frequency calculation using the '''AM1 semi-empirical molecular orbital method'''. This calculation confirmed that the transition state structure here is the true one for the Diels Alder reaction being studied, due to the fact that the imaginary frequency here at -956 cm-1 corresponds to the forming of the desired bonds.

This frequency is illustrated below. It shows the bonds being formed in a '''synchronous''' fashion. This is different to the lowest possible real frequency 147 cm-1, which is asynchronous.

The HOMO (bottom) and LUMO (top) were then plotted. The HOMO here is antisymmetric, but the LUMO is symmetric.

The optimisation of the transition state above was carried out via calculating the force constants at the start of the calculation. It was also carried out using the redundant coordinate editor to allow comparison. A similar geometry, as expected, was formed:

The partially formed C-C bond lengths for the first optimisation were 2.11920 angstroms and 2.11932 angstroms. These are very similar to those found in the second optimisation, at 2.11889 angstroms each. These compared to typical a C-C bond length of around 1.50 angstroms and a C=C bond length of around 1.32 angstroms. The van der Waal radius of a carbon atom is 1.70 angstroms. The partially formed bonds in the transition state are therefore much longer and weaker than a full C-C or C=C is.

Rep:Physical:luke4912

2009-11-13T14:51:45Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to analyse the boat transition state for this reaction, the QST2 optimisation method had to be employed. This method required the input of the reactant and product molecule for it to deduce the transition state structure. Further to this, the calculation also required every atom to be correctly labelled so it knew exactly which atoms were taking part in the bond breaking and making. It was the previously studied anti 2 orientated molecule that was modified for this calculation, so it resembled a boat structure. The picture below on the left shows an incorrectly identified optimised transition structure, this was as a result of not entering the necessary information into the calculation as just detailed. The picture below on the right is the correctly identified boat transition structure, this calculation did run to completion. The evidence of this comes from the frequency analysis, showing an imaginary frequency vibration at -840 cm-1, as expected in the script.

[[Image:X17.jpg|left]][[Image:X18.jpg|right]]

===Transition Structure Analysis===
To determine which conformers the Cope rearrangement actually proceeds by, the Intrinsic Reaction Coordinate (IRC) method was utilised. Here, the calculation took small geometric 'steps' along the gradient of the energy surface in order to determine a minimum energy pathway for the reaction. (This was done for the chair and boat structures.) Initially, the calculation was performed with 50 steps, the results however were incorrect - a minimum was not found. So the steps were increased to 200, and the following optimised structures were found.

[[Image:X19.jpg|left]][[Image:X20.jpg|right]]

The chair structure resembles the gauche 2 conformer and the boat structure matches the gauche 3 conformer, it must therefore be these two structures most found in the transition state of the Cope rearrangement.

Finally, an activation energy calculation was performed on the transition structures. Both structures were reoptimised under the B3LYP/6-31G* level of theory, from their original HF/3-21G structures. Frequency calculations were then run. The results are displayed in the table below, whilst the geometries of the two structures were similar, their activation energies differed considerably.

{| class="wikitable" border="1" align = center
|+ Activation Energy Data
! Conformer !! Calculated Ea/kcalmol-1 !! Experimental Ea/kcalmol-1
|-
| Chair || 34.19 || 33.5±0.5
|-
| Boat || 42.68 || 44.7±2.0
|}

To conclude, the calculated energies are in very good agreement with the experimental values, suggesting the calculations have all been successful and are based on sound theory.

==The Diels-Alder Cycloaddition==
Cis-butadiene reacts with ethylene in a pericyclic [4s + 2s] cycloaddition reaction to form the cyclic ene shown in the scheme below. This part of the module was concerned with plotting the molecular orbitals of this reaction to understand the mechanistic rationale. I.e. if the HOMO and LUMO interactions are favourable the reaction will happen as described, if however they are not of matching symmetry or have poor overlap, this reaction will be forbidden.

[[Image:X21.jpg|centre]]

===Molecular Orbitals===
Firstly, butadiene and ethylene were modelled and optimised in Gaussian using the semi-empirical AM1 methodology. This level of theory was sufficient since only the HOMO and LUMO orbitals were being investigated. Orbital diagrams are shown below, they have the following symmetry:

{| class="wikitable" border="1" align = center
|+ Orbital Symmetry Data
! Orbital !! Symmetry !!
|-
| Butadiene HOMO || Antisymmetric ||
|-
| Butadiene LUMO || Symmetric ||
|-
| Ethylene HOMO || Symmetric ||
|-
| Ethylene LUMO || Antisymmetric ||
|}

{|
| [[Image:X22.jpg|thumb|Butadiene HOMO]]
| [[Image:X23.jpg|thumb|Butadiene LUMO]]
| [[Image:X24.jpg|thumb|Ethylene HOMO]]
| [[Image:X25.jpg|thumb|Ethylene LUMO]]
|}

Rep:Physical:luke4912

2009-11-12T14:19:04Z

Lc407:

Rep:Physical:luke4912

2009-11-12T11:54:28Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: 0.00006 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || -231.61923477 || -231.61863392
|}

===Optimising the Boat Transition Structure===

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

[[image:dfjdffdfddkffmf.jpg|centre]]

A question stated was 'Which conformers of 1,5-hexadiene do you think they connect?'. Looking at the possible conformers, it is not possible to make any sort of prediction on this. The ''''Intrinsic Reaction Coordinate'''' (IRC) method follows the 'minimum energy path from a transition structure down to its local minimum on a potential energy surface. It creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.' ([http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]) This calculation was carried out using HF/3-21G. It was possible to see how the calculation had progressed so far, as there were structures shown for different stages of the calculation - firstly the calculation was run to 50 points along the 'IRC'. The calculation was then performed using 250 points to yield this structure (more thoroughly/accurately optimised):

[[image:dfjdffdfddkf74747fmf.jpg|centre]]

Other methods that were carried out to yield a similar transition structure were to take the last point on the IRC and run a minimisation or to make sure the force constants are computed at every stage, rather than just the start.

===Optimising the 'Boat' Transition State===

The 'boat' transition state was optimised using the ''''QST2'''' method. This method performs a calculation such that one can provide the reactant molecule and product molecule, and a transition structure is found for the reaction. For the reaction in question, it was important to specify explicitly which atoms were which when moving from the reactant molecule to the product molecule. An example of this is shown in the [http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]. This involved modification of the anti2 structure previous calculated - arranging the molcule to look like the boat transition state and numbering the reactants and products as discussed. Without this pre-rearrangement to orientate the molecule to look like the boat transition state, the calculation does not complete properly:

[[image:sdsdsdfgfgb.jpg|centre]]

The calculation was performed with the two preparatory factors considered. A good indication that the optimisation was successful was the fact that there was an imaginary frequency that corresponds to the bonds breaking/forming between the pairs of carbon atoms, at -840 cm -1:

[[image:lijrg.jpg|centre]]

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

Rep:Physical:luke4912

2009-11-12T11:48:57Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: X9 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' (RCE) method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]] pic caption needed: Animated vibration of TS Berny optimisation, RCE optimisation provided almost identical animation.

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RCE
|-
| Energy/Hartrees || X15 || X15a
|}

===Optimising the Boat Transition Structure===

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

[[image:dfjdffdfddkffmf.jpg|centre]]

A question stated was 'Which conformers of 1,5-hexadiene do you think they connect?'. Looking at the possible conformers, it is not possible to make any sort of prediction on this. The ''''Intrinsic Reaction Coordinate'''' (IRC) method follows the 'minimum energy path from a transition structure down to its local minimum on a potential energy surface. It creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.' ([http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]) This calculation was carried out using HF/3-21G. It was possible to see how the calculation had progressed so far, as there were structures shown for different stages of the calculation - firstly the calculation was run to 50 points along the 'IRC'. The calculation was then performed using 250 points to yield this structure (more thoroughly/accurately optimised):

[[image:dfjdffdfddkf74747fmf.jpg|centre]]

Other methods that were carried out to yield a similar transition structure were to take the last point on the IRC and run a minimisation or to make sure the force constants are computed at every stage, rather than just the start.

===Optimising the 'Boat' Transition State===

The 'boat' transition state was optimised using the ''''QST2'''' method. This method performs a calculation such that one can provide the reactant molecule and product molecule, and a transition structure is found for the reaction. For the reaction in question, it was important to specify explicitly which atoms were which when moving from the reactant molecule to the product molecule. An example of this is shown in the [http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]. This involved modification of the anti2 structure previous calculated - arranging the molcule to look like the boat transition state and numbering the reactants and products as discussed. Without this pre-rearrangement to orientate the molecule to look like the boat transition state, the calculation does not complete properly:

[[image:sdsdsdfgfgb.jpg|centre]]

The calculation was performed with the two preparatory factors considered. A good indication that the optimisation was successful was the fact that there was an imaginary frequency that corresponds to the bonds breaking/forming between the pairs of carbon atoms, at -840 cm -1:

[[image:lijrg.jpg|centre]]

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

Rep:Physical:luke4912

2009-11-11T22:18:58Z

Lc407:

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and in Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===
[[Image:X1.jpg|left]] [[Image:X2.jpg|right]]In this first exercise, the [3,3]-sigmatropic rearrangement of 1,5-hexadiene was studied. The aim was to locate the low energy minima and any transition structures on the reaction's potential energy surface, in order to comment on the mechanism. The scheme on the left shows the reaction and its two possible transition structures: the so-called boat and chair conformers. Gaussian software was used to model the reaction and initially the Hartree-Fock method with basis set 3-21G was employed.

The first calculation was performed on 1,5-hexadiene in the anti conformation (model shown above). Optimising the molecule gave the results summary shown below (energy displayed in Hartrees). The symmetrize function was used in order to establish the point group of the molecule: C2. This conformer is listed as 'anti 1' in Appendix 1.

[[Image:X3.jpg|centre]]

The same procedure was also performed on 1,5-hexadiene in the gauche conformation, its point group was found to be: C1. This conformer corresponds to 'gauche 3' in Appendix 1. A model of the molecule and results summary are shown below.

[[Image:X7.jpg|left]] [[Image:X8.jpg|right]]

As can be seen from the summaries, the energies of both conformers are very similar, only differing by: X9 Hartrees. Initially the anti structure might be expected to be slightly lower in energy, for steric reasons. However, it is the gauche structure that is lowest in energy, this is due to the stabilisation seen from the "gauche effect". A process whereby electron density is donated from the σC-H orbital to the п*C=C orbital. Although this weakens the ene bond, it aids to lower the energy of the molecule overall. The energies of the optimised structures using this method are nearly a perfect match with the recorded energies for the anti 1 and gauche 3 conformers listed in Appendix 1. Relative to all other possible conformers, Appendix 1 confirms gauche 3 is the lowest energy structure, with anti 1 being the second lowest (relative energy: 0.04).

A final conformer was studied in this section, it corresponds to anti 2 in Appendix 1 and is an alternative anti orientation of 1,5-hexadiene - with Ci symmetry. It is drawn below with the results summary produced from a HF/3-21G calculation. Again the energy of the structure is a near perfect match to the value listed in Appendix 1.

[[Image:X10.jpg|left]] [[Image:X11.jpg|right]]

This conformer was then subject to further calculation using a more accurate basis set: 6/31G* with B3LYP methodology. The results summary is shown below. The geometry of the B3LYP conformer did not change much at all from the less accurate HF model. On average, all of its C-C bonds elongated by ~0.001A - which given the inaccuracies of both calculations isnt a measurable difference. More notable is the difference in energy, the more accurate calculation displays a lower energy for the molecule. This is expected since a more in-depth optimisation has been performed.

[[Image:X12.jpg|centre]]

In order to compare the optimised energies with experimental values, a frequency analysis of the anti 2 molecule was performed. This was also used to determine whether the structure was at an energy minimum. The analysis is summarised in the table below, showing a breakdown of the energies from the output .log file. All the frequencies in the output were positive, showing a minimum had been found.

[[Image:X13.jpg|centre]]

===Optimising the Chair Transition Structure===

In order to create the chair transition structure, a propandiene fragment was modelled in Gaussian and was subject to HF/3-21G optimisation. Two of these fragments were then superimposed in a chair-like manor, 2.2A apart. This transition structure was then fully optimised using the TS Berny parameters, by calculating the force constants at the start of the calculation. A model of the transition structure is shown below.

[[Image:X14.jpg|centre]]

A 'redundant coordinate editor' method was then used to optimise the original structure as well. This method differed from TS-Berny by freezing the bond lengths between the terminal carbons of each fragment at 2.2A before the optimisation. The resultant molecule had almost identical geometry to the TS Berny optimised molecule, the corresponding C-C bond lengths only changing by a maximum of 0.01A. Also to note was the imaginary frequency of both molecules: -818 cm-1, this is identical to the wavenumber quoted in the script. The vibration from this frequency is animated below, it shows the Cope rearrangement reaction because the arrow vectors indicate a concerted effort to break and make bonds on the termini of the two fragments.

[[Image:X16.jpg|centre]]

{| class="wikitable" border="1" align = center
|+ Optimisation Comparison
! Property !! TS Berny !! RedCoEd
|-
| Energy/Hartrees || X15 || X15a
|}

===Optimising the Boat Transition Structure===

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

[[image:dfjdffdfddkffmf.jpg|centre]]

A question stated was 'Which conformers of 1,5-hexadiene do you think they connect?'. Looking at the possible conformers, it is not possible to make any sort of prediction on this. The ''''Intrinsic Reaction Coordinate'''' (IRC) method follows the 'minimum energy path from a transition structure down to its local minimum on a potential energy surface. It creates a series of points by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest.' ([http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]) This calculation was carried out using HF/3-21G. It was possible to see how the calculation had progressed so far, as there were structures shown for different stages of the calculation - firstly the calculation was run to 50 points along the 'IRC'. The calculation was then performed using 250 points to yield this structure (more thoroughly/accurately optimised):

[[image:dfjdffdfddkf74747fmf.jpg|centre]]

Other methods that were carried out to yield a similar transition structure were to take the last point on the IRC and run a minimisation or to make sure the force constants are computed at every stage, rather than just the start.

===Optimising the 'Boat' Transition State===

The 'boat' transition state was optimised using the ''''QST2'''' method. This method performs a calculation such that one can provide the reactant molecule and product molecule, and a transition structure is found for the reaction. For the reaction in question, it was important to specify explicitly which atoms were which when moving from the reactant molecule to the product molecule. An example of this is shown in the [http://www.ch.ic.ac.uk/wiki/index.php/Mod:phys3#Optimizing_the_.22Chair.22_and_.22Boat.22_Transition_Structures notes]. This involved modification of the anti2 structure previous calculated - arranging the molcule to look like the boat transition state and numbering the reactants and products as discussed. Without this pre-rearrangement to orientate the molecule to look like the boat transition state, the calculation does not complete properly:

[[image:sdsdsdfgfgb.jpg|centre]]

The calculation was performed with the two preparatory factors considered. A good indication that the optimisation was successful was the fact that there was an imaginary frequency that corresponds to the bonds breaking/forming between the pairs of carbon atoms, at -840 cm -1:

[[image:lijrg.jpg|centre]]

In order to calculate the activation energy of the reaction, the optimised transition structure here needs to be optimised with frequency calculations using the density-functional B3LYP method with the 6-31G* basis set. The geometry of the optimised structures for each level of theory are very similar, however there is a relatively large energy difference between them.

Rep:Physical:luke4912

2009-11-11T15:36:04Z

Lc407:

Rep:Physical:luke4912

2009-11-11T14:13:16Z

Lc407:

Rep:Physical:luke4912

2009-11-03T15:10:35Z

Lc407: /* Computational Labs: Module 3 - Transition State Chemistry */

=Computational Labs: Module 3 - Transition State Chemistry=
==Introduction==
This module focused on the structure of the transition state in the Cope Rearrangement and Diels-Alder cycloadditions. Previously used molecular mechanics methodology could not be utilised here as it can only analyse molecular geometries, it cannot give any information about bond nature, electron distribution or make any calculations about bond breaking and forming. Instead, a new method of molecular orbital based computation will be employed, whereby the Schrodinger equation is numerically solved to give details about transition state structures and where they lie on the potential energy surface.

==The Cope Rearrangement==
===Optimising the Reactants and Products===

Rep:Physical:luke4912

2009-11-03T15:06:45Z

Lc407:

Rep:Physical:luke4912

2009-11-03T14:32:01Z

Lc407: New page: =Computational Labs: Module 3 - Transition State Chemistry= ==The Cope Rearrangement==

=Computational Labs: Module 3 - Transition State Chemistry=
==The Cope Rearrangement==

Inorganic:luke4912

2009-11-03T12:42:40Z

Lc407:

=Computational Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analysis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond orbital data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the molecular orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.JPG|thumb|centre|400px|IR spectral stretches for both isomers]]

In accordance with group theory, the cis isomer shows four C=O stretching modes, all different in frequency and intensity. Whereas the trans isomer only shows one real stretching mode, since two signals have a negligible intensity and two signals have nearly identical frequencies (ie they are degenerate). Upon Gaussview animation of the trans vibrations, the degenerate signals were found to be from two pairs of carbonyls stretching asymmetrically - in effect the same movement. Overall, the calculated frequencies are all lower than the literature values, but relatively speaking they retain the same margins and patterns eg. cis stretch 1 & 2 are similar. This would lead to the conclusion that the calculations were successful, but due to model limitations and inaccuracies, the computed values are not an exact match to the experimental values.

===Symmetry===

Worth mentioning is Gaussian's symmetry result that the trans complex optimised into C1 point group geometry. This is initially strange since it is expected to have D4h symmetry. However, it is this slight deviation in symmetry that allows the two trans low-intensity absorptions to occur (at 1966 & 2025 cm-1)- these vibrations are still changing the dipole moment of the molecule. (They wouldnt be if the molecule was perfect D4h. The calculation shows all the Mo-C bond lengths are slightly different length.

One final point can be made from the frequency analysis - the presence of low frequency vibrations (at 5.87cm-1 in the cis complex and 7.03cm-1 in the trans). Much a minor absorption would be related to a freely occurring rocking motion of the PCl3 groups, happening at room temperature.

=References=

[1] - S. Lu, ''Chemical Physics'', '''2003''', 287 (3), pp 297-302

[2] - C. S. Kraihanzel, ''Inorg. Chem.'', '''1963''', 2 (3), pp 533–540

Inorganic:luke4912

2009-11-03T12:38:55Z

Lc407:

=Computional Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analsyis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond orbital data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the moleuclar orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.JPG|thumb|centre|400px|IR spectral stretches for both isomers]]

In accordance with group theory, the cis isomer shows four C=O stretching modes, all different in frequency and intensity. Whereas the trans isomer only shows one real stretching mode, since two signals have a negligible intensity and two signals have nearly identical frequencies (ie they are degenerate). Upon Gaussview animation of the trans vibrations, the degenerate signals were found to be from two pairs of carbonyls stretching asymmetrically - in effect the same movement. Overall, the calculated frequencies are all lower than the literature values, but relatively speaking they retain the same margins and patterns eg. cis stretch 1 & 2 are similar. This would lead to the conclusion that the calculations were successful, but due to model limitations and inaccuracies, the computed values are not an exact match to the experimental values.

===Symmetry===

Worth mentioning is Gaussian's symmetry result that the trans complex optimised into C1 point group geometry. This is initially strange since it is expected to have D4h symmetry. However, it is this slight deviation in symmetry that allows the two trans low-intensity absorptions to occur (at 1966 & 2025 cm-1)- these vibrations are still changing the dipole moment of the molecule. (They wouldnt be if the molecule was perfect D4h. The calculation shows all the Mo-C bond lengths are slightly different length.

One final point can be made from the frequency analysis - the presence of low frequency vibrations (at 5.87cm-1 in the cis complex and 7.03cm-1 in the trans). Much a minor absorption would be related to a freely occurring rocking motion of the PCl3 groups, happening at room temperature.

=References=

[1] - S. Lu, ''Chemical Physics'', '''2003''', 287 (3), pp 297-302

[2] - C. S. Kraihanzel, ''Inorg. Chem.'', '''1963''', 2 (3), pp 533–540

Inorganic:luke4912

2009-11-03T12:27:30Z

Lc407:

=Computional Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analsyis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond orbital data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the moleuclar orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.JPG|thumb|centre|400px|IR spectral stretches for both isomers]]

In accordance with group theory, the cis isomer shows four C=O stretching modes, all different in frequency and intensity. Whereas the trans isomer only shows one real stretching mode, since two signals have a negligible intensity and two signals have nearly identical frequencies (ie they are degenerate). Upon Gaussview animation of the trans vibrations, the degenerate signals were found to be from two pairs of carbonyls stretching asymmetrically - in effect the same movement. Overall, the calculated frequencies are all lower than the literature values, but relatively speaking they retain the same margins and patterns eg. cis stretch 1 & 2 are similar. This would lead to the conclusion that the calculations were successful, but due to model limitations and inaccuracies, the computed values are not an exact match to the experimental values.

===Symmetry===

Worth mentioning is Gaussian's symmetry result that the trans complex optimised into C1 point group geometry. This is initially strange since it is expected to have D4h symmetry. However, it is this slight deviation in symmetry that allows the two trans low-intensity absorptions to occur - these vibrations are still changing the dipole moment of the molecule.

According to group theory, an IR absorption will only occur if the resultant vibration incurs a change in dipole moment of the molecule. The two very low intensity vibrations for the trans isomer seemingly break this rule but this is assuming that the molecule is of the D4h point group. The log file reports the syymetry of the molecule as C1, and the 4 Mo-C bonds are all slightly different lengths. This means that despite the high symmetry of the vibrations, the dipole moment does change by a small amount and a low intensity absorption occurs as seen.

Low freqency absorptions occur for both isomers. For the cis at 4.45cm-1 and 6.97cm-1 and the trans at 11.39cm-1 and 20.07cm-1. These vibrations primarily involve the rocking of the PCl3 groups and would occur freely at room temperature. The energy of the photons in joules for each of the absorptions is lower than the value of kT so the vibrations would be expected to occur freely as the photons of the correct energy/frequency would be in abundance.

=References=

[1] - S. Lu, ''Chemical Physics'', '''2003''', 287 (3), pp 297-302

[2] - C. S. Kraihanzel, ''Inorg. Chem.'', '''1963''', 2 (3), pp 533–540

Inorganic:luke4912

2009-11-02T15:49:10Z

Lc407:

=Computional Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analsyis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond order data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the moleuclar orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.JPG|thumb|centre|400px|IR spectral stretches for both isomers]]

In accordance with group theory, the cis isomer shows four C=O stretching modes, all different in frequency and intensity. Whereas the trans isomer only shows one real stretching mode, since two signals have a negligible intensity and two signals have nearly identical frequencies (ie they are degenerate). Upon Gaussview animation of the trans vibrations, the degenerate signals were found to be from two pairs of carbonyls stretching asymmetrically - in effect the same movement. Overall, the calculated frequencies are all lower than the literature values, but relatively speaking they retain the same margins and patterns eg. cis stretch 1 & 2 are similar. This would lead to the conclusion that the calculations were successful, but due to model limitations and inaccuracies, the computed values are not an exact match to the experimental values.

===Symmetry===

According to group theory, an IR absorption will only occur if the resultant vibration incurs a change in dipole moment of the molecule. The two very low intensity vibrations for the trans isomer seemingly break this rule but this is assuming that the molecule is of the D4h point group. The log file reports the syymetry of the molecule as C1, and the 4 Mo-C bonds are all slightly different lengths. This means that despite the high symmetry of the vibrations, the dipole moment does change by a small amount and a low intensity absorption occurs as seen.

Low freqency absorptions occur for both isomers. For the cis at 4.45cm-1 and 6.97cm-1 and the trans at 11.39cm-1 and 20.07cm-1. These vibrations primarily involve the rocking of the PCl3 groups and would occur freely at room temperature. The energy of the photons in joules for each of the absorptions is lower than the value of kT so the vibrations would be expected to occur freely as the photons of the correct energy/frequency would be in abundance.

=References=

Inorganic:luke4912

2009-11-02T15:21:16Z

Lc407: /* Frequency Analysis */

=Computional Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analsyis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond order data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the moleuclar orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.JPG|thumb|centre|400px|IR spectral stretches for both isomers]]

The cis isomer shows 4 distinct bands in the carbonyl region, all with similar but different frequencies as well as intensities. The trans isomer also shows four different absorptions, but two are very similar both in the frequency absorbed and the intensity, and the other two are very low in intensity and expected to be negligable. From group theory, the expected number of bands for CO vibrations is 4 for the cis isomer and 1 for the trans.

The two very similar frequencies for the trans isomer can be considered the same vibration. Animation in gaussview showed that 1939cm-1 was the assymetric stretching of two trans-carbonyls, whereas 1940 was the assymetric stretching of the other two - equivalent - trans carbonyls. This is essentially the same movement, and the two movements should be degenerate as the carbonyls should map onto each other upon rotation, but, the point group is C1 rather than D4h (due to small discrepencies in the structure, see below) so the moevements are infact slightly different and hence lose their degeneracy, becoming two distinct vibrations in the calculations of gaussian.

According to group theory, an IR absorption will only occur if the resultant vibration incurs a change in dipole moment of the molecule. The two very low intensity vibrations for the trans isomer seemingly break this rule but this is assuming that the molecule is of the D4h point group. The log file reports the syymetry of the molecule as C1, and the 4 Mo-C bonds are all slightly different lengths. This means that despite the high symmetry of the vibrations, the dipole moment does change by a small amount and a low intensity absorption occurs as seen.

Low freqency absorptions occur for both isomers. For the cis at 4.45cm-1 and 6.97cm-1 and the trans at 11.39cm-1 and 20.07cm-1. These vibrations primarily involve the rocking of the PCl3 groups and would occur freely at room temperature. The energy of the photons in joules for each of the absorptions is lower than the value of kT so the vibrations would be expected to occur freely as the photons of the correct energy/frequency would be in abundance.

File:Lcmotable.JPG

2009-11-02T15:19:08Z

Lc407:

Inorganic:luke4912

2009-11-02T15:18:51Z

Lc407:

=Computional Chemistry Lab: Inorganic - Module 2=
==Optimising a Molecule of BH3==
[[Image:Lcbh3pic.jpg|thumb|right|BH3 Modelled in Gaussview]] The first task in this module was to optimise a molecule of borane - BH3. This was done in Gaussview, using the Gaussian Calculation Function with the following parameters: B3LYP methodology and 3-21G basis set. Since the molecule is relatively simple and the basis set is a poor one, the calculation was performed on the laptop and took 20 seconds. The population analysis output file can be viewed here:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BH3_POP.LOG]]

The results summary showed an RMS gradient <0.001 therefore the calculation was a success and the optimisation had reached the energy minimum. From the output file, the different B-H bond lengths and H-B-H bond angles were found, these are tabulated below:

{| class="wikitable" border="1" align = "middle"
|+ BH3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.19A
|-
| Bond Length || 1-3 || 1.19A
|-
| Bond Length || 1-4 || 1.19A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

The data proves all the B-H bonds are equivalent and thus the molecule must have a D3h point group.

===Frequency Analysis ===
A frequency analysis was then performed on BH3, this is the process of differentiating between the possible maxima, minima and transition states within the energy profile of the molecule. When BH3 is optimised the first derivative of the energy is set to zero. Graphically speaking, the second derivative must then be calculated to determine the nature of this stationary point. For instance, if the calculation output frequencies are all positive, a minimum energy has been found; if they are all negative then a maximum energy has been found. A mixture means the point is a transition state.

In order to minimise calculation time on the laptop, the same methodology and basis set used for the optimisation was used for the frequency analysis. This way the program didnt need to re-optimise the molecule again. The results are discussed in the vibrational analysis section below, in summary: all the frequencies were positive meaning the minimum energy orientation had been found.

=== Vibrational Analysis ===
Analysis of the molecular vibrations of BH3 was carried out using the frequency analsyis output file. In the table below, all six vibrations have been animated and their respective frequencies and intensities reported. The table shows all the vibrational frequencies are positive and therefore the calculation was a success, the lowest energy orientation has been found. Also to note is the degeneracy of some vibrations as well as a zero intensity mode, therefore an IR spectrum of this molecule may not contain six peaks.

[[Image:Lcbh3vibtable.jpg|thumb|centre|500px|Vibrations of BH3.]]

Natural bond order data was also recorded - bonding orbital occupancy and energy is reported in the table below. This is accompanied with a diagram of BH3 showing the NBO charges on each atom.
[[Image:Lcnbopic.jpg|left|300px]]
{| class="wikitable" border="1" align = "middle"
|+
! Orbital !! Atoms !! Occupancy !! Energy/Ha
|-
| BD || B1-H2 || 2.00 || -0.437
|-
| BD || B1-H3 || 2.00 || -0.437
|-
| BD || B1-H4 || 2.00 || -0.437
|-
| CR || B1 || 2.00 || -6.645
|-
| LP* || B1 || 0.00 || 0.678
|}

In the initial stages of a Gaussian calculation, Gaussview does not show any bonds in a molecule. This however is just a convention and should not be noticed - if the distance between two atoms is larger than Gaussview's predefined definition of a bond length it will simply not draw a bond in place, this does not mean however there is no interaction between the atoms. A bond could be defined as a favourable electronic interaction between two atoms.

=== Molecular Analysis ===
The BH3 molecule was subject to one further analysis, of its molecular orbitals. By refining the Gaussian calculation with keywords: "pop=full" the seven lowest energy BH3 molecular orbitals were calculated and animated below (with their symmetry labels). A molecular orbital diagram of the molecule accompanies the animations so the correlation between real MOs and LCAO MOs can be seen. The diagrams show good agreement between models, however the real MOs are somewhat misleading when visualised. For instance, the 3a' real MO shows roughly equal bonding contributions from the H & B orbitals, whereas the LCAO MO predicts small contributions from the H orbitals. This highlights the differences between a theoretical and mathematical model.

{|
| [[Image:Lcbh3mo1.jpg|thumb|110px|2a'1]]
| [[Image:Lcbh3mo2.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo3.jpg|thumb|110px|1e']]
| [[Image:Lcbh3mo4.jpg|thumb|110px|1a''2]]
| [[Image:Lcbh3mo5.jpg|thumb|110px|3a'1]]
| [[Image:Lcbh3mo6.jpg|thumb|110px|2e']]
| [[Image:Lcbh3mo7.jpg|thumb|110px|2e']]
|}

[[Image:Lcbh3modiagram.jpg|thumb|500px|centre|MO diagram for BH3.]]

==Optimising a Molecule of BCl3==
[[Image:Lcbcl3pic.jpg|thumb|left|Model of BCl3.]][[Image:Lcbcl3summary.jpg|thumb|250px|right|Output results summary for BCl3.]]The next stage of this module was to improve the accuracy of calculations using the simple molecule BCl3. This involved optimising the molecule using the same method as before (B3-LYP) but with a more accurate basis set: LanL2MB. This basis set imposes a pseudo-potential on the chlorine atoms, the result is: the calculation is restricted and will only take into account the valence electron bonding interactions with the boron atom. This is merely to shorten the calculation time. Captured on the right is the calculation summary, showing it took 15 seconds to complete and the RMS gradient once again is satisfactory. The molecule has been assigned the D3h point group.

From the log file:[[https://www.ch.ic.ac.uk/wiki/index.php/Image:LUKE_BCL3_OPT.LOG]] the following properties of the molecule were deduced:

{| class="wikitable" border="1" align = "middle"
|+ BCl3 Properties
! !! Atoms !! Value
|-
| Bond Length || 1-2 || 1.87A
|-
| Bond Length || 1-3 || 1.87A
|-
| Bond Length || 1-4 || 1.87A
|-
| Bond Angle|| 4-1-3|| 120.0o
|-
| Bond Angle|| 4-1-2|| 120.0o
|-
| Bond Angle|| 3-1-2|| 120.0o
|}

Again, all the bonds are equivalent in this molecule. The literature<ref>XXXXX</ref> quotes the exact same bond angles and B-H bond lengths of 1.75A which are very close to the calculated values. The model is in good agreement with the experimental evidence, this is expected since BCl3 is a simple molecule and thus the basis set is accurate enough.

=Isomers of Mo(CO)4L2=

In this section of the module two octahedral complexes of molybdenum were investigated: the cis and trans isomers of Mo(CO)4L2 where L = PCl3. Images of these molecules are shown below, the investigation was centered on their structures, relative energies (for thermal stability comparison) and IR spectra. Due to the complex nature of these molecules their calculations had to be submitted to SCAN for overnight computing. To begin with however, a "loose" or inaccurate optimisation was performed to gain a rough interpretation of their geometries. Both isomers were optimised using the B3-LYP method and pseudo-potential basis set LanL2MB, these parameters gave a short calculation time. The resultant optimised molecules were then subject to a more accurate calculation, by changing the basis set to LanL2DZ and restricting it to "int=ultrafine". Keyword "scf=conver=9" was also inputted which relates to the high definition Gaussian is required to compute the moleuclar orbitals with. Finally, it was known the molecule had several potential energy minima close to each other, so the molecules had to be manually altered to avoid Gaussian calculating to a false minimum. This was achieved by changing the PCl3 groups torsion angles and orientation.

The new optimised molecules were shown to contain no bonds between the P and Cl atoms, however this was discussed earlier and is irrelevant to the analysis. One final step to the improve the results included changing the keyword in the calculation to "extrabasis" this allows gaussian to incorporate P's d-orbitals. The results from this optimisation are clear: more basis functions are used and thus a more accurate geometry is calculated - the P-Cl bonds shorten slightly. (Expected since Cl will back-bond into vacant Pd-orbitals.

{|
| [[image:Lcmocis.jpg|thumb|cis Mo(CO4)(PCl3)2]]
| [[image:Lcmotrans.jpg|thumb|trans Mo(CO4)(PCl3)2]]
|}

===Structural Analysis===
From the LOG files, the final optimised molecules differ in energy by only 2kJ/Mol (the trans isomer having the lower energy of: -1637350.5 kJ/mol). Although the trans isomer is expected to be lower in energy, given the inherent assumptions and inaccuracies of this computational work, such a small difference in energy can be deemed negligible. The trans isomer should be lower in energy since it would cause less steric hinderance within the molecule, this effect may have been easier to see with larger L ligands like PPh3 for instance. From 2nd year synthetic labs, thermal cis to trans isomerisation was seen in Mo(CO)4(PPh3)2.

===Frequency Analysis===
Similar for BH3 a frequency analysis was run on the molecules. The resultant frequencies (for C=O stretches) are tabulated below for both isomers, along with the literature<ref>XXXXXX</ref> values. All the frequencies are positive indicating the zero point on the potential energy surface was a minimum.

[[Image:Lcmotable.jpg|thumb|centre|IR spectral stretches for both isomers]]

The cis isomer shows 4 distinct bands in the carbonyl region, all with similar but different frequencies as well as intensities. The trans isomer also shows four different absorptions, but two are very similar both in the frequency absorbed and the intensity, and the other two are very low in intensity and expected to be negligable. From group theory, the expected number of bands for CO vibrations is 4 for the cis isomer and 1 for the trans.

The two very similar frequencies for the trans isomer can be considered the same vibration. Animation in gaussview showed that 1939cm-1 was the assymetric stretching of two trans-carbonyls, whereas 1940 was the assymetric stretching of the other two - equivalent - trans carbonyls. This is essentially the same movement, and the two movements should be degenerate as the carbonyls should map onto each other upon rotation, but, the point group is C1 rather than D4h (due to small discrepencies in the structure, see below) so the moevements are infact slightly different and hence lose their degeneracy, becoming two distinct vibrations in the calculations of gaussian.

According to group theory, an IR absorption will only occur if the resultant vibration incurs a change in dipole moment of the molecule. The two very low intensity vibrations for the trans isomer seemingly break this rule but this is assuming that the molecule is of the D4h point group. The log file reports the syymetry of the molecule as C1, and the 4 Mo-C bonds are all slightly different lengths. This means that despite the high symmetry of the vibrations, the dipole moment does change by a small amount and a low intensity absorption occurs as seen.

Low freqency absorptions occur for both isomers. For the cis at 4.45cm-1 and 6.97cm-1 and the trans at 11.39cm-1 and 20.07cm-1. These vibrations primarily involve the rocking of the PCl3 groups and would occur freely at room temperature. The energy of the photons in joules for each of the absorptions is lower than the value of kT so the vibrations would be expected to occur freely as the photons of the correct energy/frequency would be in abundance.