ChemWiki - User contributions [en]

Rep:Mod3jsm108

2010-12-17T16:05:12Z

Jsm108: /* IRC analysis */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but with calculation of the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product.<ref name="orbital overlap">A Density Functional Theory Study of Secondary Orbital Overlap in Endo Cycloaddition Reactions. An Example of a Diels−Alder Reaction between Butadiene and Cyclopropene {{DOI|10.1021/jo9620223}}</ref> The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state. A diagram summarising this interaction is shown below:

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

In the Diels-Alder transition state calculations there a numerous things that have been negelected. For example, the role of solvents in the reaction could be quite large, and vary the transition states and their energies to some extent. This would change the nature of the reaction and the leading product, depending on the solvent the reaction is carried out in. If I had more time, I would investigate this further to see the extent of effect solvent has on the reaction.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T16:02:19Z

Jsm108: /* The reaction between cyclohexa-1,3-diene and maleic anhydride */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product.<ref name="orbital overlap">A Density Functional Theory Study of Secondary Orbital Overlap in Endo Cycloaddition Reactions. An Example of a Diels−Alder Reaction between Butadiene and Cyclopropene {{DOI|10.1021/jo9620223}}</ref> The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state. A diagram summarising this interaction is shown below:

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

In the Diels-Alder transition state calculations there a numerous things that have been negelected. For example, the role of solvents in the reaction could be quite large, and vary the transition states and their energies to some extent. This would change the nature of the reaction and the leading product, depending on the solvent the reaction is carried out in. If I had more time, I would investigate this further to see the extent of effect solvent has on the reaction.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:57:31Z

Jsm108: /* Conclusion */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state. A diagram summarising this interaction is shown below:

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

In the Diels-Alder transition state calculations there a numerous things that have been negelected. For example, the role of solvents in the reaction could be quite large, and vary the transition states and their energies to some extent. This would change the nature of the reaction and the leading product, depending on the solvent the reaction is carried out in. If I had more time, I would investigate this further to see the extent of effect solvent has on the reaction.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:41:43Z

Jsm108: /* Transition state calculations */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state. A diagram summarising this interaction is shown below:

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:38:43Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:27:02Z

Jsm108: /* Conclusion */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=
It can be seen that computational calculations are extremely useful. It is possible to accurately predict the transition state of a reaction via numerous methods, as well as to trace the energy surface to find which conformer will be formed from the found transition state. A range of different values such as the activation energy can also be calculated for transition states, allowing us to differentitate between high and low energy transition state pathways. Molecular orbital calculations of the reactants and transition states give a good picture about the orbital interactions that have occured to form the molecular orbitals of the transition state.

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:21:55Z

Jsm108: /* Diels-Alder reaction */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

The van der Waals radius is larger that the bond lengths in the molecule, but smaller than the bond length for the fragments C-C bond distances (part formed bonds). This was the expected result.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:17:26Z

Jsm108: /* Diels-Alder reaction */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii {{DOI|10.1021/j100785a001}}</ref>

The values for aveage C-C bond lengths match well with the bond lengths measured in the reactants, as expected. The transition state bond lengths sit between the values, as expected as well, because they would be inbetween sp2 and sp3 bonds.

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T15:13:13Z

Jsm108: /* Diels-Alder reaction */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="van de waals">Van der Waals Volumes and Radii{{DOI|10.1021/j100785a001}}</ref>

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:57:08Z

Jsm108: /* Diels-Alder reaction */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond length
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

It can be seen that the values seen above match well with predictions about what would happen to the bond lengths and angles going from the reactants to the products. The fragment bond length is a lot longer than any of the other C-C bonds. This is the case because these bonds are only part formed. All the C-C bonds have more or less become equal in the transition state. This matches well with the electron movement in the mechanism shown above for the reaction. The butadiene angle has also decreased going from the reactant to the transition state, and has moved closer to 120°, which would be my prediction for the bond angle within the hexene product.

Typical sp3 C-C bond lengths have been found to be 1.54A and typical sp2 C-C bondlengths have been found to be 1.34A.<ref name="C-C bond lengths">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32</ref>

The van der Waals radius of the C atom has been found to be 1.7 A.<ref name="vdw">A. Bondi,Van der Waals Volumes and Radii, J. Phys. Chem, 68, 1964, p441–51[http://pubs.acs.org/doi/pdf/10.1021/j100785a001]</ref>

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:43:38Z

Jsm108: /* Obtained values and calulations */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle (°)
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle (°)
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:43:14Z

Jsm108: /* Obtained values and calulations */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:42:34Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Obtained values and calulations===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>. There is less steric hindrance when going via the chair transition state when compared to the boat transition state.

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:40:36Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="Cope reaction">Chair and boat transition states for the Cope rearrangement {{DOI|10.1021/ja00221a092}}</ref>

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod:hgmd3

2010-12-17T14:38:29Z

Jsm108:

<h1>Module 3</h1>
<h4>by Hayleigh Gascoigne</h4>
Computational chemistry was used in this module to find transition states for reactions. This was dome using various methods, such as TS (Berny), frozen co ordinates and QST2. These transitions states were confirmed by the presence of one imaginary frequency in the frequency analysis.

<h2>The Cope Rearrangement</h2>
The Cope rearrangement of 1,5-hexadiene is seen below. The carbon atoms are numbered so the rearrangement can be seen more easily.

[[Image:Reaction_schemehg508.gif]]

This reaction proceeds via a [3,3]-sigmatropic shift in a concerted fashion where the transition state is either a boat or chair structure, as shown below.
[[Image:Chairboathg508.jpg]]

First, an anti periplanar conformer of the reactant was drawn and optimised using HF/3-21G level of theory. Using the same level of theory, a gauche conformer was drawn. The molecules were symmetrised and their point groups noted. This can be seen in the table below.
{| class="wikitable" border="1" align="centre"
|+ ''The energy and point group of two conformers of 1,5-hexadiene''
! Conformer !! <jmol> <jmolAppletButton> <uploadedFileContents>React_antihg508.mol</uploadedFileContents> <text>Anti</text> </jmolAppletButton> </jmol> !! <jmol> <jmolAppletButton> <uploadedFileContents> React_gauchehg508.mol</uploadedFileContents> <text>Gauche</text> </jmolAppletButton> </jmol>
|-
| Energy (a. u. ): || -231.6925 || -231.6917
|-
| Point Group: || Ci || C2
|}

Generally, anti periplanar conformers have lower energy. This is because there is less steric hindrance with this structure. However, it was found in this case that a gauche structure had the lowest energy. Gauche structures have the lowest energy is some cases because, it is favourable to have H-H interactions at certain distances, and this particular structure allows lots of these kinds of Van der Waals interactions. However, the gauche conformer shown above was not the conformer with the lowest energy. The structure with the lowest energy was found to be the structure shown below, and is known as 'gauche3' in the reference table. It has the point group C1 and the energy -231.6927 a. u.
This corresponds to the one with the lowest energy in the reference table given. The previous anti corresponds to 'anti2' and the gauche corresponds to 'gauche2'.

<jmol> <jmolAppletButton> <uploadedFileContents>Gauchelowhg508.mol</uploadedFileContents> <text>Gauche</text> </jmolAppletButton> </jmol>

The structure with the lowest energy was then optimised with a higher level of theory, B3LYP/6-31G*. This structure can be seen below. It has the energy -234.6117 a. u. This cannot be compared to the previous energies, as a different level of theory was used.

<jmol> <jmolAppletButton> <uploadedFileContents>2ndoptantihg508.mol</uploadedFileContents> <text>Optimised anti2</text> </jmolAppletButton> </jmol>

By comparison, the structures look virtually identical. However, certain dihedral and bond angles as well as bond lengths were measured and the results can be seen in the table below. The numbers correspond to the numbers seen on the reactant molecule in the above diagram.

{| class="wikitable" border="1" align="centre"
|+ ''A comparison of angles and bond lengths in optimised structures of the anti2 conformer''
! Property !! 1st Opt (B3LYP/3-21G)!! 2nd Opt (B3LYP/6-31G*)
|-
| Dihedral Angle: C1-C2-C3-C4 || 114.7o || 118.5o
|-
| Bond Angle: C1-C2-C3 || 124.8o || 125.3o
|-
| Bond Angle: C2-C3-C4 || 111.3o || 112.7o
|-
| Bond length: C1-C2 || 1.32Å || 1.33Å
|-
| Bond Length: C2-C3 || 1.51Å || 1.50Å
|-
| Bond Length: C3-C4 || 1.55Å || 1.55Å
|}

The angles have been quoted to an accuracy of 0.1o and the angles 0.01Å. It would be incorrect to quote them to more decimal places, as the calculations made to receive these results are not that accurate.

A frequency calculation was then carried out on the anti2 conformer to see if only real frequencies existed. This was confirmed as there were no negative frequencies. A table of the most important vibrations are shown below.

{| class="wikitable" border="1" align="centre"
|+ ''Vibrations of the anti2 conformer''
! Frequency (cm-1) !! Animated Vibration!! Description
|-
| 1734 || [[Image:1734hg508.gif]] || C=C stretch
|-
| 3031 || [[Image:3031hg508.gif]] || alkane C-H stretch
|-
| 3080 || [[Image:3080hg508.gif]] || alkane C-H stretch
|-
| 3137 || [[Image:3137hg508.gif]] || C-H stretch
|-
| 3155 || [[Image:3155hg508.gif]] || alkene C-H stretch
|-
| 3234 || [[Image:3234hg508.gif]] || alkene C-H stretch
|}

The literature<ref name="IR">IR Absorptions for Representative Functional Groups[http://www.chemistry.ccsu.edu/glagovich/teaching/316/ir/table.html]</ref> says that alkane C-H stretches occur at 2950-2800cm-1 whilst alkene C-H stretches occur at 3100-3010cm-1. The C=C stretch is said to occur at 1690-1630cm-1. Therefore it can be seen that all the calculated frequencies are higher than the tabulated ones. This is expected as it is due to the estimations that the calculation makes about the nature of the bonds. It estimates them as harmonic oscillators, whereas in reality they are anharmonic oscillators. Another reason that the calculated frequencies may be higher is the complexity of the basis set used. The accuracy of the calculated frequencies would be improved by improving the basis set, but this computationally expensive and this is why it has not been done.

The spectrum has also been visualised below.

[[Image:Anti2spectrumhg508.jpg]]

The energies from the part of the log file named 'Thermochemistry' are shown below.

{| class="wikitable" border="1" align="centre"
|+ ''Thermochemistry''
! Energy !! Value (a. u.)
|-
| Sum of electronic and zero-point Energies || -234.469212
|-
| Sum of electronic and thermal Energies || -234.461856
|-
| Sum of electronic and thermal Enthalpies || -234.460912
|-
| Sum of electronic and thermal Free Energies || -234.500821
|}

The Sum of electronic and zero-point Energies is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal Energies is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal Enthalpies contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal Free Energies includes the entropic contribution to the free energy (G = H - TS).

After the optimisation of the reactants, the transition state chair and boat structures were also optimised.
First a fragment, CH2CHCH2, was optimised using the HF/3-21G level of theory. Two of these were pasted into the same window, and arranged into a chair conformation. This structure was then optimised separately in two different ways.

The first was by computing the force constants at the beginning of the calculation and this only works well if the initial guess structure is close to the real one. The optimisation was carried out to a 'TS (Berny)'. The force constants were calculated once and Opt=NoEigen was typed into the additional keywords. Once optimised, the structure gave an imaginary frequency of 818cm-1. This is animated below, and it can be seen that it corresponds to the connection/disconnection of the appropriate bonds for the cope rearrangement.

[[Image:818hg508.gif]]

The second method was done by using the redundant coordinate editor. The reaction coordinate was frozen, using the keywords Opt=ModRedundant, and then the rest of the molecule was minimised. Once the molecule is relaxed, the coordinates can be unfrozen and the molecule optimisation can be started again. The carbon atoms involved in the reaction coordinate were frozen at 2.2Å apart. The optimised chair transition state of this molecule also had a vibrational frequency at -818cm-1.

The bond forming/bond making bond length of the first optimised transition structure was 2.02046Å and for the transition structure optimised in the second way was 2.02079Å. It is usual to quote these lengths to two decimal places, and so therefore these two lengths are the same.
Other bond lengths were the same, and bond angles were also the same to the required accuracy.

The energy of the transition state for structure optimised with the first method was -231.61932248 a. u. whereas the energy of the second transition state was -231.61932159 a. u. These energies are therefore the same as the small discrepancy is due to errors.
It can be seen therefore that both of these methods are valid since they reach the same optimised transition state. They have their advantages and disadvantages which must be considered when using them for other molecules. The second method is more time consuming, but may be easier to get the right structure in the end. The first method is only good if the initial structure is close to the minima required.

The QST2 method was used to optimise the boat structure. The anti2 structure was opened and copied and pasted in the same window. These were viewed alongside each other and the atoms on the product were renumbered according to the numbering system seen at the beginning of the page. The job was submitted but with optimisation to a 'TS(QST2)'. The job failed, since the reactant nor the product resembled the boat transition structure. So the structure was then modified to this effect. The central dihedral angle was changed to 0o , and the inside C-C-C bond angles changed to 100o. This job was submitted to receive the transition structure. To prove this was the transition structure, a frequency analysis was done. One imaginary frequency was visualised at -840cm-1. This means the transition structure was found. The vibration is shown below. The connection/disconnection of the bonds is asynchronous.

[[Image:840hg508.gif]]

The boat transition state is thought to form the gauche1 conformer, and the chair transition state is thought to form gauche2. This is the closest structure that they resemble however, it is hard to tell what will happen in reality. However, the Intrinsic Reaction Coordinate which allows you to follow the minimum energy path from the transition structure to its local minimum on a potential energy surface. A series of points of small geometry steps along the steepest part of the slope are created. For the first calculation 50 points were taken along the IRC, as the default of 6 is not enough.
Once this job had finished, it was seen that a minimum had not been reached. There were only 26 steps, so the job didn't terminate for the reason that it reached the limit of steps. In order to find the minima, two different methods were invoked. The first was to run the IRC again with the same method but with starting from the last structure from the previous calculation. This was done, but a minima was still not found. So, a different method was then used. The IRC was rerun from the beginning structure but this time calculating the force constants along every step. This turned out to be more reliable, though more expensive, since the optimum structure was found in 47 steps. This was confirmed to be a minimum when the structure was optimised and the resulting molecule was the same. The molecule is shown below:

<jmol> <jmolAppletButton> <uploadedFileContents>optchairmethod3hg508.mol</uploadedFileContents> <text>Minima</text> </jmolAppletButton> </jmol>

It can be seen that this corresponds to the gauche2 structure.

Here is the progression of the IRC by the second method.

[[Image:IRCchairmethod3.jpg]]
[[Image:IRCchairmethod31.jpg]]

Starting from the HF/3-21G optimised structures of the chair and boat, the structures were optimised again using the B3LYP/6-31G* level of theory. Comparisons for the two differently optimised chair and boat structures are shown below.

{| class="wikitable" border="1" align="centre"
|+ ''Chair transition state optimisation''
! !! 3-21G !! 6-31G*
|-
| Energy (a. u.) || -231.6193 || -234.5570
|-
| C-C-C Bond Angle || 120.5o || 120.0o
|-
| Bond forming/breaking Bond Length || 2.02Å || 1.97Å
|-
| C-C Bond Length || 1.39Å || 1.41Å
|}

{| class="wikitable" border="1" align="centre"
|+ ''Boat transition state optimisation''
! !! 3-21G !! 6-31G*
|-
| Energy (a. u.) || -231.6028 || -234.5431
|-
| C-C-C Bond Angle || 121.7o || 122.3o
|-
| Bond forming/breaking Bond Length || 2.14Å || 2.21Å
|-
| C-C Bond Length || 1.38Å || 1.39Å
|}
It can be seen that the geometries between the two optimisations are similar, and there is not much difference between the angles and lengths. The energies however are markedly different. These cannot really be compared since a different level of theory was used to work each out. The literature<ref name="lit1">K. Morokuma, W. T. Borden, D. A. Hrovat, Chair and boat transition states for the Cope rearrangement, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475.[http://pubs.acs.org/doi/pdf/10.1021/ja00221a092]</ref> shows that the interallyl bond length should be 2.062Å. Therefore it can be seen that the values obtained here are close to this, and therefore the calculation and basis set used were good since they closely resemble reality.
The activation energies were worked out at both levels of theory and for each transition structure, and are compared to experimental values in the table below.

{| class="wikitable" border="1" align="centre"
|+ ''Activation Energies at 0K (kcal/mol)''
! !! HF/3-21G !! B3LYP/6-31G* !! Experiment
|-
| Chair|| 45.93|| 34.32 || 33±0.5
|-
|Boat|| 56.29|| 43.05 || 44.7±2.0
|}

The activation energy for the chair transition state is lower than for the boat. This is also what is seen in the literature<ref name="lit1">K. Morokuma, W. T. Borden, D. A. Hrovat, Chair and boat transition states for the Cope rearrangement, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475.[http://pubs.acs.org/doi/pdf/10.1021/ja00221a092]</ref>. The chair transition state gives less steric hindrance and so has a lower activation energy barrier.
The calculated values are close to literature for the calculations where the higher level of theory is used. Therefore, it can be seen that this basis set is better and works well for this system as it creates accurate results. However, using the lower level of theory first and then going on to use this structure for the higher level of theory is a good method, as it is more computationally efficient.

Using the thermochemistry data, a table has been compiled showing the energies corresponding to the one in the reference table given. The energies match very closely, and so the correct transition states and the correct anti2 structure were found.

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

<h2>The Diels Alder Cycloaddition</h2>
The Diels-Alder reaction is a cycloaddition between a diene and a dienophile. π orbitals of the dieneophile are used to form new σ bonds with π orbitals of the diene. The HOMO/LUMO of one of the fragment interacts with the HOMO/LUMO of the other and forms two new bonding and anti-bonding MOs.
The most simple of these reactions is between ethylene and cis-butadiene. This will be studied along with a case where the reactants have substitents, such as is the case for maleic anhydride (the dienophile) and cyclohexadiene (the diene).
Transition structures for these reactions was found by using the AM1 semi-emperical molecular orbital method.
<h4>Ethylene and Cis-butadiene</h4>
Here is the reaction scheme.

[[Image:basicreactionhg508.gif]]

Firstly cis-butadiene and ethylene were optimised separately with the AM1 method, and the molecular orbitals were plotted.

{| class="wikitable" border="1" align="centre"
|+ ''Molecular Orbitals''
! !! Molecule !! HOMO!! LUMO
|-
| Cis-butadiene|| [[Image:moleculeanglehg508.jpg]] || [[Image:HOMOcisbutahg508.jpg]] || [[Image:LUMOcisbutahg508.jpg]]
|-
| || || Antisymmetric || Symmetric
|-
|Ethylene|| [[Image:moleculeangle2hg508.jpg]]|| [[Image:HOMOethylenehg508.jpg]]|| [[Image:LUMOethylenehg508.jpg]]
|-
| || || Symmetric || Antisymmetric
|}

The transition structure was found using the freeze co-ordinates method. Firstly, the TS (Berny) method was used, but the minima was not located, and so the structure was not optimised. The two optimised fragments were pasted into the same window, and frozen at 2.2Å apart, then optimised to a minimum. The structure was unfrozen, and then optimised as a transition state. This was a better method, since the minimum was found. This was confirmed by the presence of one negative frequency at -956.96cm-1 in the frequency analysis.
This frequency is shown below. It can be seen that the bond formation is synchronous, which is evidence for the fact that this reaction is concerted.

[[Image:vibtsiihg508.gif]]

The lowest real frequency is seen at 147cm-1 and this is animated below. It is seen that it is a wagging mode rather than the stretching mode that was seen above. The real frequency is also different in that it is asynchronous.

[[Image:vibtsii147hg508.gif]]

This are the HOMO and the LUMO and it can be seen that the HOMO is antisymmetric.
{| class="wikitable" border="1" align="centre"
|+ ''Molecular Orbitals of transition state''
! HOMO !! LUMO
|-
| [[Image:HOMOiihg508.jpg]] || [[Image:LUMOiihg508.jpg]]
|}

These are formed by interaction of the MOs with the same symmetry, as these are the only ones that are allowed. The HOMO of the cis-butadiene interacts with the LUMO of the ethylene, as these are both antisymmetric and hence forming the HOMO of the transtion state. Whilst the LUMO of the cis-butadiene interacts with the HOMO of ethylene, as these are both symmetric, thus forming the symmetric LUMO.

The molecule can be seen here. <jmol> <jmolAppletButton> <uploadedFileContents>Dielsaldertshg508.mol
</uploadedFileContents> <text>Transition State</text> </jmolAppletButton> </jmol>

Here are some of the angles and lengths, in order that the structure can be analysed.

{| class="wikitable" border="1" align="centre"
|+ ''Geometry of Transition State''
! !! From Fragments !! Transition State
|-
| Partly formed bond length || N/A || 2.12Å
|-
| Ethylene C=C length || 1.33Å || 1.38Å
|-
| Butadiene C=C length || 1.34Å || 1.38Å
|-
| Butadiene C-C length || 1.45Å || 1.40Å
|-
| Butadiene C=C-C angle || 125.7o || 121.2o
|}

The C-C distance for the formation of the new bond was found to be 2.12Å. This is significantly longer than any of the other C-C bond lengths, and this is obviously because this is the transition structure, and the bonds have not formed yet. It can be seen in the transition state that the various C-C bond lengths are more uniform than the C-C bond lengths from the individual fragments, again, indicative of a transition state, as the bond lengths in the product would be expected to be approximately equal. The bond angle has reduced in the transition state, which is also expected, as the internal angles within a hexagon (or six membered carbon ring) are 120o.

A typical sp2 C-C bond length was found in the literature to be 1.3Å whilst a typical sp3 bond length was 1.54Å<ref name="sp">H. O. Pierson, Handbook of Carbon, Graphite, Diamond and Fullerenes, 1993, p32[http://books.google.co.uk/books?id=jPT6JADCqgwC&pg=PA30&lpg=PA30&dq=sp3+carbon+bond+length&source=bl&ots=xPXAMHUXrh&sig=9u27owFpQe72CizzYEulNL2aIXQ&hl=en&ei=2-TbTL20AoWK4gbHuP3OCA&sa=X&oi=book_result&ct=result&resnum=8&ved=0CEkQ6AEwBw#v=onepage&q=sp3%20carbon%20bond%20length&f=false]</ref>. In the above fragments, it can be seen that bond length measurements are close to the literature, but in the transition state, The Van der Waals radius of the carbon atom is 1.70Å<ref name="vdw">A. Bondi,Van der Waals Volumes and Radii, J. Phys. Chem, 68, 1964, p441–51[http://pubs.acs.org/doi/pdf/10.1021/j100785a001]</ref>. This is smaller than the partly formed bond length, but larger than the bonds already formed. This is the expected outcome.

<h4>Cyclohexa-1,3-diene and Maleic Anhydride</h4>
These molecules react to give the endo adduct as the major product. The regiochemistry is controlled by π orbitals on the dienophile, by virtue of their symmetry. The presence of these extra orbitals contributes to the bonding and so gives that structure extra stabilisation. This is known as the secondary orbital effect. It is thought that as the reaction is kinetically controlled, the exo product has a higher energy. Using the frozen co ordinates method once again, both of these transition structures were located. They were confirmed as transition states because both had one negative frequency.

The endo structure had a negative frequency at -806.92cm-1
[[Image:vibendotshg508.gif]]

The exo structure had a negative frequency at -812.23cm-1
[[Image:vibexotshg508.gif]]

The important bond lengths for the endo structure are shown.

[[Image:Endo_bond_lengthshg508.jpg]]

The C-C through space bond length between the (C=O)-O-(C=O) and the CH=CH was found to be 2.89Å.

The important bond lengths for the exo structure are shown.

[[Image:Exo_bond_lengthshg508.jpg]]

The C-C through space bond length between the (C=O)-O-(C=O) and the CH2-CH2 was found to be 2.94Å.

{| class="wikitable" border="1" align="centre"
|+ ''HOMOs of the transition structures''
! Endo !! Exo
|-
| [[Image:HOMOendohg508.jpg]] || [[Image:HOMOexohg508.jpg]]
|}

The endo structure optimisation shows that the fragments are closer together (shown by the bond forming bond length and the C-C through space length in particular), thus supporting the idea that this is the major product, as it is favourable for the reactants to be in a close proximity and therefore react. The other bond lengths are about the same, but due to the orientation in the exo structure, the longer C-C makes the C-C through space bond longer. The energy for the endo structure was -0.05150445 a. u. and the energy for the exo structure was -0.05041928 a. u.

It can be seen that in the endo structure, the two alkene bonds are positioned closely to the two carbonyl groups whereas in the exo structure, they are positioned further away. It is more favourable to have them close because this allows for the secondary orbital overlap effect to come about as there is significant orbital overlap between the orbitals of the diene and the orbitals of the dienophile<ref name="secondary">Branko S. Jursic,A Density Functional Theory Study of Secondary Orbital Overlap
in Endo Cycloaddition Reactions, J. Org. Chem. 1997, 62, p3046-3048[http://pubs.acs.org/doi/pdf/10.1021/jo9620223]</ref>.

In the (C=O)-O-(C=O) part of the molecule, for exo, it seen that there is no electron density, and thus no positive orbital overlap, and so this structure is less stabilised. There is more strain in the exo structure, than the endo, which is another reason for its increased instability.

Overall, it can be seen that the endo structure, although thermodynamically less stable, is the product observed, mainly due to the positive orbital overlap, which allows the orbitals of the same symmetry on the two fragments for the endo structure to overlap, and hence stabilise this structure. In addition to this, there is contribution from the substituents, making the transition state even more stabilised. The exo structure does not have this kind of stabilisation and hence is strained.

In conclusion, it can be seen that gaussian can predict the most stable structure based on the energy, and human observation of the orbitals. However, it is limited since there is an error of ~0.038 a. u. and so if there is only a small energy difference between the two transition states, it can be hard to tell which one is the major one.
Gaussian is only making calculations on this one molecule as created in gaussview, whereas in reality there would be many more molecules all affecting each other and all in slightly different conformations, and so it would be better if the calculation took into account statistical mechanics using a boltzmann distribution.
Of course, all the energy calculations are approximated and at different levels depending on the basis set used. And so, all the energy approximations can be improved and be closer to the energies seen in reality if a better basis set is used.

<h2>References</h2>
<references/>

Rep:Mod3jsm108

2010-12-17T14:37:54Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

It can be seen again that the values calculated match extremely well with the values given in the reference table. The values calaulcted at the higher level of theory match more closely to the literature values than the values calculated at the lower level of theory. From this approach it can be seen that using a low level of theory to map the energy surface, followed by a higher level of theory to give accurate results is a good method and efficient method.

From the data it can be seen that the chair transition state has a lower activation energy than the boat transition state, which agrees with the literature.<ref name="lit1">K. Morokuma, W. T. Borden, D. A. Hrovat, Chair and boat transition states for the Cope rearrangement, J. Am. Chem. Soc., 1988, 110 (13), pp 4474–4475.[http://pubs.acs.org/doi/pdf/10.1021/ja00221a092]</ref>

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:30:29Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
!colspan="3"|'''Boat transition state'''
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:29:59Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:29:40Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|!colspan="3"|'''Chair transition state'''
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:28:51Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.71
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.16
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.61
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:24:16Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:23:54Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539539
| align="center" | -231.532568
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:22:04Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.6925352
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170273
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:20:05Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.6193225
| align="center" | -231.466700
| align="center" | -231.461340
| align="center" | -234.556983
| align="center" | -234.414929
| align="center" | -234.409008
|-
| '''Boat TS'''
| align="center" | -231.6028022
| align="center" | -231.450922
| align="center" | -231.445295
| align="center" | -234.5430931
| align="center" | -234.402342
| align="center" | -234.396008
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:15:57Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

From the data in the table above, it was possible to calculate the activation energies for the chair and the boat transition states at 0K and 298.15K. The results are shown in the table below.

''' Summary of activation energies (in kcal/mol) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''HF/3-21G'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''B3LYP/6-31G*'''
| width="125" align="center" | '''Expt.'''
|-
| ''' '''
| width="125" align="center" | '''at 0 K '''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| width="125" align="center" | '''at 0 K'''
|-
| '''ΔE (Chair)'''
| align="center" | 45.70
| align="center" | 44.69
| align="center" | 34.06
| align="center" | 33.17
| align="center" | 33.5 ± 0.5
|-
| '''ΔE (Boat)'''
| align="center" | 55.60
| align="center" | 54.76
| align="center" | 41.96
| align="center" | 41.32
| align="center" | 44.7 ± 2.0
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-17T14:05:46Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

Thermochemistry data has also been calculated for the chair and boat transition states and is displayed below:

Chair transition state- lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat transition state- lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair transition state- higher basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat transition state- higher basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

Using all of the data collected, a table has been drawn showing all the energies and values calculated. The values I have calculated match very well with the values found in the reference table, and so it can be deduced that the correct strucures were successfully found.

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:33:32Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

The same values were also found for the lower basis set calculation:

Sum of electronic and zero-point Energies= -231.539539
Sum of electronic and thermal Energies= -231.532566
Sum of electronic and thermal Enthalpies= -231.531622
Sum of electronic and thermal Free Energies= -231.570909

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Chair lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair better basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:31:45Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Chair lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Boat lower basis set
Sum of electronic and zero-point Energies= -231.450922
Sum of electronic and thermal Energies= -231.445295
Sum of electronic and thermal Enthalpies= -231.444350
Sum of electronic and thermal Free Energies= -231.479112

Chair better basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:30:05Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Chair lower basis set
Sum of electronic and zero-point Energies= -231.466700
Sum of electronic and thermal Energies= -231.461340
Sum of electronic and thermal Enthalpies= -231.460396
Sum of electronic and thermal Free Energies= -231.495206

Chair better basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:28:06Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.91916753 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Chair better basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:23:43Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Chair better basis set
Sum of electronic and zero-point Energies= -234.414929
Sum of electronic and thermal Energies= -234.409008
Sum of electronic and thermal Enthalpies= -234.408064
Sum of electronic and thermal Free Energies= -234.443814

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:22:24Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
| -231.6193225
| -234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
| -818
| -566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
| -231.6028022
| -234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
| -840
| -530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:22:00Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

{| border="1"
|Chair transition state
|
|
|----
|Property
|HF/3-21G
|B3LYP/6-31G*
|----
|Energy (Hartrees)
|-231.6193225
|-234.556983
|----
|C-C-C bond angle ()
|120.5
|120
|----
|Fragments bond distance (A)
|2.02
|1.97
|----
|C-C bond length (A)
|1.39
|1.41
|----
|Imaginary frequency (cm-1)
|-818
|-566
|----
|Boat transition state
|
|
|----
|Property
|HF/3-21G
|HF/6-31G
|----
|Energy (Hartrees)
|-231.6028022
|-234.5430931
|----
|C-C-C bond angle ()
|121.6
|122.3
|----
|Fragments bond distance (A)
|2.14
|2.21
|----
|C-C bond length (A)
|1.38
|1.39
|----
|Imaginary frequency (cm-1)
|-840
|-530
|----
|}

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:17:06Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrum1jsm10.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 73 cm-1 to 3234 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

File:Anti2optbetterorbitalsetirspectrum1jsm10.jpg

2010-12-16T15:16:53Z

Jsm108:

Rep:Mod3jsm108

2010-12-16T15:14:49Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

Sum of electronic and zero-point Energies= -234.469212
Sum of electronic and thermal Energies= -234.461856
Sum of electronic and thermal Enthalpies= -234.460912
Sum of electronic and thermal Free Energies= -234.500822

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:13:53Z

Jsm108: /* The Cope Rearrangement */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.61170273
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:07:18Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:06:54Z

Jsm108: /* Changing the level of theory */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

Boat better basis set
Sum of electronic and zero-point Energies= -234.402342
Sum of electronic and thermal Energies= -234.396008
Sum of electronic and thermal Enthalpies= -234.395063
Sum of electronic and thermal Free Energies= -234.431097

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T15:02:22Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|3.904°
|----
|12 bond length
|1.316 A
|1.334 A
|0.018 A
|----
|23 bond length
|1.509 A
|1.504 A
|0.005 A
|----
|34 bond length
|1.552 A
|1.548 A
|0.004 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T14:58:09Z

Jsm108: /* Optimising the reactants and products */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.53°
|°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.53°
|°
|----
|12 bond length
|1.316 A
|1.334 A
| A
|----
|23 bond length
|1.509 A
|1.504 A
| A
|----
|34 bond length
|1.552 A
|1.548 A
| A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T14:24:16Z

Jsm108: /* Data */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.711°
|4.085°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.711°
|4.085°
|----
|12 bond length
|1.316 A
|1.338 A
|0.022 A
|----
|23 bond length
|1.509 A
|1.507 A
|0.002 A
|----
|34 bond length
|1.552 A
|1.555 A
|0.003 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Changing the level of theory===
The chair and boat transition structures were reoptimized using the B3LYP/6-31G* level of theory frequency calculations were also completed. The HF/3-21G optimized structures were used as starting point. The geometries and the difference in energies between the reactants and transition states at the two levels of theory were compared, and displayed below.

Looking at the results in the table, the geometries of the transitions states do not change dramatically when the level of theory is changed. However, there is quite a large difference in the energy of the transition states between the theory levels.

The activation energies were calculated for both the chair and boat transition states

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-16T14:17:44Z

Jsm108: /* IRC analysis */

3rd year computational: module 3

Josh McNicoll

00551754

__TOC__

=Introduction=
The following project shows the use of computational methods to find transition states in different reactions. Numerous different methods are used such as TS (Berny), the frozen co-ordinate method and QST2. A frequency analysis confirms a transition state by computing one imaginary frequency, which relates to the reaction being studied. The conformation of the product can also be predicted using computational methods via an IRC calculation.

=The Cope Rearrangement=
The cope rearrangement is a [3,3]-sigmatropic shift rearrangement.

[[Image:Coperearrangementjsm108.gif]]

==Optimising the reactants and products==

Different conformations of 1,5-hexadiene are possible, each with a different associated energy.

Initially an anti periplanar conformer was drawn and minimised using HF/3-21G level of theory. The energy of the structure was recorded and the molecule was symmetrised to find the point group of the molecule. This method was followed for a gauche conformer. As seen the anti periplanar conformer has the lower energy when compared to the gauche conformer. This is due to the anti periplanar conformer having less steric repulsion due to the arrangement. However, the lowest energy conformer was found to be a gauche conformer (gauche 3). The low energy is probably due to favourable Van de Waals interactions between hydrogens in the molecule overriding the slightly higher steric strain. The Ci anti 2 conformer was then drawn and optimised at the HF/3-21G level of theory, and then followed by the B3LYP/6-31G* level of theory.

All of the results are summarised in the table below:

{| border="1"
!Conformation
!Theory level
!Computed energy (Hartrees)
!Literature energy from appendix (Hartrees)
!Point group
!Structure
!Conformer
!Comments
|----
|Anti conformer
|HF/3-21G
| -231.6926024
| -231.69260
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Anti_first_moleculejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 1
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Gauche conformer
|HF/3-21G
| -231.691667
| -231.69167
|C2
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Gauche_optjsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Lowest energy conformer
|HF/3-21G
| -231.6926612
| -231.69266
|C1
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Lowestenergygauchejsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|gauche 3
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|HF/3-21G
| -231.6925352
| -231.69254
|Ci
|Same as below
|anti 2
|The computed energy matches perfectly with the appendix energy for the conformer
|----
|Ci anti 2 conformation
|B3LYP/6-31G*
| -234.5596966
| -234.611710
|Ci
|<jmol><jmolApplet><title>Lowest conformation structure</title><color>white</color>
<size>200</size><script>zoom 5;moveto 4 0 2 0 90 120;spin 2;</script>
<uploadedFileContents>Betteroptofsnti2jsm108.mol</uploadedFileContents>
</jmolApplet></jmol>
|anti 2
|The computed energy matches well with the appendix energy for the conformer
|----
|}

The geometries for the anti 2 conformers when optimised with different levels of theory were almost identical. The geometry changes between the optimised structures can be measured by comparing the dihedral angles in the molecules. These are measured for 4 atoms, and so 3 angles can be measured along the chains; carbons 1,2,3 and 4, carbons 2,3,4 and 5, and carbons 3,4,5 and 6. Measured parameters for the HF/3-21G and B3LYP/6-31G* levels of theory are shown in the table below:

{| border="1"
!Carbons used for measurement
!Low level theory HF/3-21G
!High level theory B3LYP/6-31G*
!Difference
|----
|1234 dihedral angle
|114.626°
|118.711°
|4.085°
|----
|2345 dihedral angle
|180.0°
|180.0°
|0°
|----
|3456 dihedral angle
|114.626°
|118.711°
|4.085°
|----
|12 bond length
|1.316 A
|1.338 A
|0.022 A
|----
|23 bond length
|1.509 A
|1.507 A
|0.002 A
|----
|34 bond length
|1.552 A
|1.555 A
|0.003 A
|----
|}

Energy difference between HF/3-21G and B3LYP/6-31G* levels for the Ci anti 2 conformation: 2.86716145 Hartrees

It can be seen that the higher level of theory gives slightly different bond lengths and dihedral angles. As seen from the table, the bond lengths are more accurate at the lower level theory than the angles. If the lower level of theory is used, bond lengths can accurately be recorded to 0.1 A, and angles to the nearest whole degree. The higher level of theory managed to locate a slightly lower energy minimum for the conformer also.

[[Image:Anti2optbetterorbitalsetirspectrumjsm108.jpg|thumb|right|IR spectrum of the optimised anti 2 conformer at B3LYP/6-31G* level]]

The optimized Ci anti 2 conformation B3LYP/6-31G* structure was used to run a frequency calculation at the same level of theory. All vibrations are real and positive, ranging from 70 cm-1 to 3245 cm-1. This result supports the idea that the optimised geometry is an energy minimum. The spectrum calculated is shown to the right.

Using the output file, the following values were found in the 'thermochemistry' section:

The sum of electronic and zero-point energies= -234.416252 a.u.

The sum of electronic and thermal energies= -234.408952 a.u.

The sum of electronic and thermal enthalpies= -234.408008 a.u.

The sum of electronic and thermal free energies= -234.447897 a.u.

The Sum of electronic and zero-point energies= the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE).

The Sum of electronic and thermal energies= the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes (E = E + Evib + Erot + Etrans).

The Sum of electronic and thermal enthalpies= contains an extra correction for RT (H = E + RT), which is particularly important when looking at dissociation reactions.

The Sum of electronic and thermal free energies= includes the entropic contribution to the free energy (G = H - TS)

==Optimizing the "Chair" and "Boat" Transition Structures ==
===Chair===
An allyl fragment (CH2CHCH2) was drawn and optimized using the HF/3-21G level of theory. This molecule was then pasted twice into a new window and orientated so that they look roughly like the chair transition state. The transition state was then found using 2 different methods.

{|
[[Image:Chairtsvibsmallerjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from optimisation to a TS (Berny)]]
|
[[Image:Chairvibsmallersecondmethodjsm108.gif|thumb|left|500px|Illustration of chair imaginary frequency -818 cm-1 from using the frozen coordinate method]]
|}

The distance between the terminal ends of the allyl fragments was set to 2.2 Å. Hartree Fock and basis set 3-21G theory was used to optimise to a transition state- TS (Berny). The force constants were calculated once and opt=noeigen was added to the additional keywords (to allow an imaginary frequency to be calculated).

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02045 Å

Energy of transition state= -231.61932247 Hartrees

The structure was then optimized to the transition structure using the frozen coordinate method. The fragments distances were frozen at 2.2 Å and the molecule was optimised using the opt=modredundant option. The frozen bonds were then relaxed and a transition state optimisation was set up.

Imaginary frequency calculated= -818 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.02044 Å

Energy of transition state= -231.61932227 Hartrees

It can be seen that both methods have yielded the same results. The imaginary frequency is the same for both methods, and the bond lengths between the fragments are also the same to 4 decimal places, which is higher than the accuracy the lengths are normally recorded to. The transition state energies are also very similar and similar to 6 decimal places, again much higher than the accuracy the energy is normally recorded to.

Both methods are seen to be successful, but each one has a disadvantage. Luckily, the first method worked well for me here, but a good guess at the transition state is needed for the method to work successfully. The second method does not need as good a guess, but is a lot more time consuming to carry out.

Looking at the chair transition state, it is thought to connect the gauche 2 conformer, although in reality this is hard to say.

[[Image:Boatvibsmalljsm108.gif|thumb|right|500px|Illustration of boat imaginary frequency -840 cm-1 from the QST2 method]]

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

[[Image:Numberedcopereacjsm108.gif]]

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

Imaginary frequency calculation= -840 cm-1

The vibration was animated and seen to correspond to the Cope rearrangement.

Optimised distance between the terminal ends of the allyl fragments= 2.13940 Å

Energy of transition state= -231.60280217 Hartrees

Looking at the boat transition state, it is thought to connect the gauche 1 conformer, although again in reality this is hard to say.

===IRC analysis===
The intrinsic reaction coordinate allows you to follow the minimum energy path from a transition state down to its local minimum on a potential energy surface. Initially the calculations for the boat and chair transition states were computed with 50 steps. When the jobs had completed it could be seen that neither the boat nor the chair had managed to find a minimum. This left a couple of options left to continue with. The first method was to run an optimisation on the final structure from the initial IRC calculation. The second method was to start the IRC calculation again but calculation the force constants at each step. The results are shown in the tables below.
====IRC chair====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial (50 steps)
| -231.619322
|[[Image:InitialIRCenergyjsm108.jpg|thumb|left|Chair IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.691667
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6916644
|[[Image:Alwayscalcircenergyjsm108.jpg|thumb|left|Chair IRC force constants always]]
|It can be seen that this method has accurately found a minimum energy structure.
|----
|}
====IRC boat====
{| border="1"
!IRC type
!Energy (a.u.)
!Energy surface
!Comments
|----
|Initial
| -231.6750656
|[[Image:Boatircinitialircenergyjsm108.jpg|thumb|left|Boat IRC initial]]
|As seen from the energy graph, a minimum was not found. It can be seen that 50 steps is not high enough for a minimum to be found.
|----
|An optimisation was then run on the final structure
| -231.6830255
|Optimisation
|It can be seen that this method has accurately found a minimum energy structure.
|----
|Force constant always
| -231.6506762
|[[Image:Boatfcsalwaysenergyjsm108.jpg|thumb|left|Boat IRC force constants always]]
|As seen from the energy graph, this method was not successful at producing a minimum energy structure.
|----
|}
====IRC analysis====
It can be seen that the optimisation of the final structures of the initial IRCs yielded the lowest energy minima each time, and this method has been quick and effective at locating the minima for both the boat and chair transition states. Calculating the force constants at every step was successful for the chair transition state, but was not successful for the boat transition state. A minimum was found, but this was a higher energy minimum when compared to the optimisation.

The chair transition state has minimised into the gauche 2 conformation.

The boat transition state has not minimised to any of the conformers successfully. The calculation would need to be repeated initially with many more steps to be able to find the minimum, and then perhaps optimised again afterwards to be able to get a accurate minimum energy.

===Data===

{| border="1" cellspacing="1" cellpadding="10"
|-
| ''' '''
!colspan="3"|'''HF/3-21G'''
!colspan="3"|'''B3LYP/6-31G*'''
|-
| ''' '''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
| width="125" align="center" | '''Electronic energy'''
| width="125" align="center" | '''Sum of electronic and zero-point energies'''
| width="125" align="center" | '''Sum of electronic and thermal energies'''
|-
| ''' '''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
| ''' '''
| width="125" align="center" | '''at 0 K'''
| width="125" align="center" | '''at 298.15 K'''
|-
| '''Chair TS'''
| align="center" | -231.61932159
| align="center" | -231.466696
| align="center" | -231.461336
| align="center" | -234.55698130
| align="center" | -234.414905
| align="center" | -234.408980
|-
| '''Boat TS'''
| align="center" | -231.60280243
| align="center" | -231.450927
| align="center" | -231.445299
| align="center" | -234.54309307
| align="center" | -234.402342
| align="center" | -234.396009
|-
| '''Reactant (''anti2'')'''
| align="center" | -231.69253529
| align="center" | -231.539540
| align="center" | -231.532568
| align="center" | -234.61170278
| align="center" | -234.469212
| align="center" | -234.461856
|}

=The Diels Alder Cycloaddition=
The Diels-Alder reaction is a cycloaddition reaction. The reaction occurs between a diene and a dienophile, with the HOMO/LUMO from the diene interacting the the HOMO/LUMO of the dienophile. The simplest Diels-Alder reaction occurs between ethene and cis-butadiene.

[[Image:DAreactionschemejsm108.gif]]
==Ethene and cis-butadiene==
Ethene and cis-butadiene were optimised using the semi-empirical AM1 method, and the molecular orbitals were visualised. The results are shown in the table below:

{| border="1"
!Molecule
!Energy of molecule
!HOMO energy
!HOMO image
!HOMO symmetry (with respect to σv plane)
!LUMO energy
!LUMO image
!LUMO symmetry (with respect to σv plane)
|----
|Ethene
|0.02619028
| -0.38775
|[[Image:Ethenehomojsm108.jpg|thumb|left|Ethene HOMO]]
|Symmetric
|0.05283
|[[Image:Ethenelumojsm108.jpg|thumb|left|Ethene LUMO]]
|Antisymmetric
|----
|Cis-butadiene
|0.04879738
| -0.3438
|[[Image:Cisbutadienehomocorrectjsm108.jpg|thumb|left|Cis butadiene HOMO]]
|Antisymmetric
|0.01707
|[[Image:Cisbutadienelumocorrectjsm108.jpg|thumb|left|Cis butadiene LUMO]]
|Symmetric
|----
|}

It is known that only orbitals of the same symmetry can interact, and so it can be seen that the LUMO of ethene can interact with the HOMO of cis-butadiene, and the HOMO or ethene can interact with the LUMO of cis-butadiene.

==Diels-Alder reaction==
The transition state for the reaction was calculated. A bicyclic system was first drawn and optimised. The CH2-CH2 fragment was then removed. The fragment end distances were first guessed at 2.15 A and the molecule was optimised to a TS (Berny).

This yielded a good result, with one imaginary frequency at -818 cm-1. The vibration matched with the Diels-Alder reaction. It can be seen that the bond formation is synchronous, agreeing with the fact that the Diels-Alder reaction has concerted bond forming.

The lowest real frequency is observed at 167 cm-1. This is seen to be a rocking of the "ethene" part of the transition state.

Transition state energy= -231.60320855 Hartrees

{|
[[Image:DAvib1111111111jsm108.gif|thumb|left|350px|Imaginary vibration at -818 cm-1 relating to the Diels-Alder reaction]]
|
[[Image:DAhomojjsm108.jpg|thumb|left|350px|HOMO]]
|
[[Image:DAlumojjsm108.jpg|thumb|left|350px|LUMO]]
|}

The transition state HOMO is observed to be antisymmetric in symmetry. It can be deduced that the HOMO has been formed from the interaction between the LUMO of ethene and the HOMO of cis-butadiene because they are both antisymmetric. The transition state LUMO is observed to be symmetric, and so has been formed from the interaction between the HOMO of ethene and the LUMO of cis-butadiene because they are both symmetric.

Some measured parameters for the reactants and the transition state have been summarised in the table below.

{| border="1"
|Measurement
|Reactants
|Transition state
|----
|Fragment C-C bond length
| -
|2.21 A
|----
|Ethene C=C bond lenght
|1.33 A
|1.38 A
|----
|Butadiene C=C bond length
|1.34 A
|1.37 A
|----
|Butadiene C-C bond length
|1.45 A
|1.39 A
|----
|Butadiene C-C=C angle
|125.6°
|121.5°
|----
|}

==The reaction between cyclohexa-1,3-diene and maleic anhydride==
Cyclohexa-1,3-diene and maleic anhydride react in a Diels-Alder reaction to give primarily the endo product. The reaction is supposed to be kinetically controlled so that the exo transition state should be at a higher energy. The reaction scheme is shown below:

[[Image:Hexadienemaleicreacschemejsm1088.gif]]

===Transition state calculations===
Bicyclo systems were built and optimised. The -CH2-CH2- fragments were then removed depending on which transition state was wanted. The interfragment distances were guessed at 2.2 A the strcutres were optimised to a TS (Berny) to characterise the transition structures. The transition structures were confirmed by running a frequency analysis and looking for one imaginary frequency that related to the reaction in focus. Bond lengths and distances along with the HOMOs and LUMOs were also calculated and recorded. All the information is displayed in the table below.

{| border="1"
|Property
|Exo
|Endo
|----
|Product energy (Hartrees)
| -0.15990927
| -0.16017083
|----
|Transition state energy (Hartrees)
| -0.05041985
| -0.0515048
|----
|Imaginary frequency vibration cm-1
| -812
| -806
|----
|Imaginary frequency vibration animation
|[[Image:Exoproductvibjsm108.gif|thumb|left|350px|Exo vibration]]
|[[Image:Endotsvibsmalljsm108.gif|thumb|left|350px|Endo vibration]]
|----
|Lowest real frequency cm-1
|61
|62
|----
|Lowest real frequency description
|Rocking of cyclohexadiene fragment
|Rocking of cyclohexadiene fragment
|----
|Fragment bond distance
|2.17
|2.16
|----
|(C=O)-C-(C=O) through space distance
|2.27963
|2.27923
|----
|C=C distance
|1.39676
|1.39724
|----
|C-C bridge distance
|1.52208
|1.52297
|----
|HOMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOHOMOCORRECTJSM108.jpg|thumb|left|350px|Exo HOMO]]

Antisymmetric
|[[Image:ENDOHOMOCORRECTJSM108.jpg|thumb|left|350px|Endo HOMO]]

Antisymmetric
|----
|LUMO (highlighted carbons are the bridging CH2-CH2 carbons)
|[[Image:EXOLUMOCORRECTJSM108.jpg|thumb|left|350px|Exo LUMO]]

Antisymmetric
|[[Image:ENDOLUMOCORRECTJSM108.jpg|thumb|left|350px|Endo LUMO]]

Antisymmetric
|----
|}

The biggest result that agrees with the endo product being favoured is the transition state energy and the product energy. The endo product has a lower transition state energy than the exo transition state energy, and also a product energy lower than the exo product energy.

The fact that the endo transition state has a lower energy means that, if the reaction is under kinetic control, the endo product will favour as it has a lower kinetic barrier than the exo product.

The endo fragment has slightly shorter fragment bond distances when compared to the exo product, meaning the fragments are slightly closer together. This is a logical observation as this agrees with the above result.

Looking at the HOMOs for both transition structures, there is a difference in the (C=O)-O-(C=O) region of the products. The exo product has no visible electron density in this region, whereas the endo product has visible electron density in this region. From this, it can be concluded that there is significant secondary orbital overlap in the endo product when compared to the exo product. The secondary orbital overlap in the endo transition structure will stabilise the transition state and cause a lowering in the energy. This stabilisation is not seen for the exo transition state.

[[Image:Overlapsinendoproductjsm108.gif]]

=Conclusion=

=References=
<references />

Rep:Mod3jsm108

2010-12-15T17:41:59Z

Jsm108: /* Transition state calculations */

File:Overlapsinendoproductjsm108.gif

2010-12-15T17:41:52Z

Jsm108:

Rep:Mod3jsm108

2010-12-15T17:33:15Z

Jsm108: /* Transition state calculations */

Rep:Mod3jsm108

2010-12-15T17:32:33Z

Jsm108: /* Transition state calculations */

Rep:Mod3jsm108

2010-12-15T17:27:35Z

Jsm108: /* Diels-Alder reaction */

Rep:Mod3jsm108

2010-12-15T17:26:37Z

Jsm108: /* Ethene and cis-butadiene */

Rep:Mod3jsm108

2010-12-15T17:23:29Z

Jsm108: /* Diels-Alder reaction */