Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

The Chair transition state was taken as a the structure input, and maximum energy along a specified reaction path was found, having also taken into account zero-point energies and so forth. Having produced all of the quantities needed for a variational transition state theory calculation. Initially 50 points were plotted along the IRC to see how the calculation progressed, this can be seen in the IRC graph below; With 50 points the calculation had not reached a minium geometry yet as illustrated in the graphs and images below.

I chose to try option two, the IRC was restarted and 400 points were specified in the hope that this would be enough until the structure optimises to reach a minimum.

(iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches.

Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

ii)ts berny, semi empirical, AM1 , once, opt=noeigen.

[[Image:ethylenenumbered.jpg|centre|300px|]]
table of angles....

Make sure correct number of protons on carbon atoms, only 2 on bonding carbons.
to characterise the transition structure.

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:tqvib1n.jpg|centre|200px|]]
|[[Image:tqvibout.jpg|centre|200px|]]
|}

Confirm you have obtained a transition structure for the Diels Alder reaction!
Only one negative frequency is obtained at...-955.01 cm-1....
guessing the transition structure
Once you have obtained the correct structure, plot the HOMO as in (i).

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanilumo.jpg|centre|300px|]]
|[[Image:shanihomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

iii) Exo ts berny semi empirical opt=noeigen constants=once
EXO
ii) Computation of the Transition State geometry for the prototype reaction and an examination of the nature of the reaction path.

The transition structure has an envelope type structure, which maximizes the overlap between the ethylene π orbitals and the π system of butadiene. One way to obtain the starting geometry is to build the bicyclo system (b) and then remove the -CH2-CH2- fragment. One must then guess the interfragment distance (dashed lines) and optimize the structure, but use any method you wish, based on the tutorial above, to characterise the transition structure. Confirm you have obtained a transition structure for the Diels Alder reaction!
guessing the transition structure
guessing the transition structure

Once you have obtained the correct structure, plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

(iii) To Study the regioselectivity of the Diels Alder Reaction

Cyclohexa-1,3-diene 1 undergoes facile reaction with maleic anhydride 2 to give primarily the endo adduct. The reaction is supposed to be kinetically controlled so that the exo transition state should be higher in energy.
regioslectivity
regioslectivity

Locate the transition structures for both 3 and 4. Compare the energies of the endo and exo forms.

Transition states for 3 and 4 exo and endo products.

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Exo''' [[Image:shaniexonumbered.jpg|centre|300px|]]
|'''Endo'''[[Image:shaniendonumbered.jpg|centre|300px|]]
|- align="center"
|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>esodiels.mol</uploadedFileContents>
</jmolApplet></jmol>'''EXO transition state'''
|<jmol><jmolApplet><title>Pentahelicene</title><color>white</color>
<size>150</size><script>zoom 200; cpk -20;</script>
<uploadedFileContents>endodiels.mol</uploadedFileContents>
</jmolApplet></jmol>'''Endo transition state'''
|- align="center"
|[[Image:shaniexohomo.jpg|centre|300px|]]
|[[Image:shaniendohomo.jpg|centre|300px|]]
|- align="center"
|HOMO EXO
|HOMO ENDO
|}

Measure the bond lengths of the partly formed σ C-C bonds and the other C-C distances. Make a sketch with the important bond lengths. Measure the orientation, (C-C through space distances between the C=O-CO-C=O- fragment of the maleic anhydride and the C atoms of the “opposite” -CH2-CH2- for the exo and the “opposite” -CH=CH- for the endo). The structure must be a compromise between steric repulsions of the -CH2-CH2- fragment and the maleic anhydride for the exo versus secondary orbital interactions between the π systems of -CH=CH- and -C=O-CO-C=O- fragment for the endo.

Plot the HOMO as in the previous exercise. Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”?
[edit] Suggested Discussion

Use this template as a guide. Screen images can be saved from the GaussView File menu.

For cis butadiene:
Plot the HOMO and LUMO and determine the symmetry (symmetric or anti-symmetric) with respect to the plane.

For the ethylene+cis butadiene transition structure:
Sketch HOMO and LUMO, labeling each as symmetric or anti symmetric.

Show the geometry of the transition structure, including the bond-lengths of the partly formed σ C-C bonds.

What are typical sp3 and sp2 C-C bondlengths? What is the van der Waals radius of the C atom? What can you conclude about the C-C bondlength of the partly formed σ C-C bonds in the TS.

Illustrate the vibration that corresponds to the reaction path at the transition state. Is the formation of the two bonds synchronous or asynchronous? How does this compare with the lowest positive frequency?

Is the HOMO at the transition structure s or a?

Which MOs of butadiene and ethylene have been used to form this MO? Explain why the reaction is allowed.

For the cyclohexa-1,3-diene reaction with maleic anhydride:
Give the relative energies of the exo and endo transition structures. Comment on the structural difference between the endo and exo form. Why do you think that the exo form could be more strained? Examine carefully the nodal properties of the HOMO between the -C=O-CO-C=O- fragment and the remainder of the system. What can you conclude about the so called “secondary orbital overlap effect”? (There is some discussion of this in Ian Fleming's book 'Frontier Orbitals and Organic Chemical Reactions').

Further discussion:
What effects have been neglected in these calculations of Diels Alder transition states?

File:Shaniendonumbered.jpg

2009-02-27T18:19:11Z

Sb1106:

2009-02-27T17:07:11Z

Sb1106:

Rep:Mod:whitelies

2009-02-27T17:06:50Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

ii)ts berny, semi empirical, AM1 , once, opt=noeigen.

[[Image:tspart2.jpg|centre|300px|]]

Make sure correct number of protons on carbon atoms, only 2 on bonding carbons.
to characterise the transition structure.

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:tqvib1n.jpg|centre|200px|]]
|[[Image:tqvibout.jpg|centre|200px|]]
|}

Confirm you have obtained a transition structure for the Diels Alder reaction!
Only one negative frequency is obtained at...-955.01 cm-1....
guessing the transition structure
Once you have obtained the correct structure, plot the HOMO as in (i).

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanilumo.jpg|centre|300px|]]
|[[Image:shanihomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

iii) Exo ts berny semi empirical opt=noeigen constants=once

File:Tqvibout.jpg

2009-02-27T17:02:38Z

Sb1106:

File:Tqvib1n.jpg

2009-02-27T17:02:19Z

Sb1106:

Rep:Mod:whitelies

2009-02-27T17:02:07Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

ii)ts berny, semi empirical, AM1 , once, opt=noeigen.

[[Image:tspart2.jpg|centre|300px|]]

Make sure correct number of protons on carbon atoms, only 2 on bonding carbons.
to characterise the transition structure.

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:tqvib1n.jpg|centre|200px|]]
|[[Image:tqvibout.jpg|centre|200px|]]
|}

Confirm you have obtained a transition structure for the Diels Alder reaction!
Only one negative frequency is obtained at...-955.01 cm-1....
guessing the transition structure
Once you have obtained the correct structure, plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

iii) Exo ts berny semi empirical opt=noeigen constants=once

File:Tspart2.jpg

2009-02-27T16:53:34Z

Sb1106:

Rep:Mod:whitelies

2009-02-27T16:53:19Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

ii)ts berny, semi empirical, AM1 , once, opt=noeigen.

[[Image:tspart2.jpg|centre|300px|]]

Make sure correct number of protons on carbon atoms, only 2 on bonding carbons.
to characterise the transition structure. Confirm you have obtained a transition structure for the Diels Alder reaction!
Only one negative frequency is obtained at...-955....
guessing the transition structure
Once you have obtained the correct structure, plot the HOMO as in (i). Rotate the molecule so that the symmetry and nodal properties of the system can be interpreted, and save a copy of the image.

iii) Exo ts berny semi empirical opt=noeigen constants=once

Rep:Mod:whitelies

2009-02-27T16:44:36Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|- align="center"
|LUMO
|HOMO
|}

Rep:Mod:whitelies

2009-02-27T16:44:04Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

Lumo is symmetric through C1 plane

Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|300px|]]
|[[Image:shanibutadienehomo.jpg|centre|300px|]]
|}

File:Shanibutadienehomo.jpg

2009-02-27T16:43:29Z

Sb1106:

File:Shanibutadienelumo.jpg

2009-02-27T16:43:14Z

Sb1106:

Rep:Mod:whitelies

2009-02-27T16:41:57Z

Sb1106: /* The Diels Alder cycloaddition */

Shahania Begum

='''Module 3 Physical computational lab'''=

=='''Transition states'''==
For the following set of computational experiments, the transition structures in larger molecules have been explored. Molecular orbital-based methods, numerically solving the Schrodinger equation, and locating transition structures based on the local shape of a potential energy surface have been used to describe bonds being made and broken, and changes in bonding type / electron distribution. As well as showing what transition structures look like, reaction paths and barrier heights have also been calculated.

==Exercises==
The Cope rearrangement of 1,5-hexadiene has been studied as an example of a chemical reactivity problem.

The low-energy minima and transition structures on the 1,5-hexadiene's potential energy surface were located in order to determine the preferred reaction mechanism.

This [3,3]-sigmatropic shift rearrangement occurs in a concerted fashion via either a "chair" or a "boat" transition structure, with the "boat" transition structure lying several kcal/mol higher in energy.

The B3LYP/6-31G* level of theory, is later used to reproduce activation energies and enthalpies which are in remarkably good agreement with experiment.

==The Cope rearrangement tutorial==

In GaussView, a molecule of 1,5-hexadiene with an "anti" linkage for the central four C atoms was constructed and the structure was cleaned then optimised using the HF/3-21G level of theory.
The energy and the point group of this structure were noted;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti 1,5-hexadiene '''
|- align="center"
|[[Image:shanianti4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69097
|- align="center"
|'''Point group'''
|- align="center"
| C1
|}

Another molecule of 1,5-hexadiene with a "gauche" linkage was created. Again the structure was optimised using the HF/3-21G level of theory and the point group symmetry was recorded.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene '''
|- align="center"
|[[Image:shanigauche4.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69153
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

From comparing the energies of the "anti" and "gauche" conformers initially it would be expected that the gauche conformer would be lower in energy due to the additional stabilisation caused by hyperconjugation and bent bonds from the overlapping orbitals-the Gauche effect. The energy of the Gauche conformer is -231.96153 a.u, with a point group of C2 symmetry. The anti conformer has an energy of -231.69097 a.u. From comparing the final energies of the optimised anti and gauche conformers it can be seen that the Gauche conformer has a slightly more negative energy than the anti conformer rendering it more stable with the lower energy.

Calculated activation energies and enthalpies normally use the lowest energy conformation of a reactant molecule as a reference. Based on the above results, it could be predicted that the lowest energy conformation of 1,5-hexadiene might be a gauche conformation perhaps with the double bonds anti-symmetric with respect to each other rather than parallel in the example above.

This hypothesis was tested out below;

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Gauche 1,5-hexadiene (hypothesis test) '''
|- align="center"
|[[Image:shanigauche2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69167
|- align="center"
|'''Point group'''
|- align="center"
| C2
|}

It appears as thought the hypothesised gauche structure is slightly more stable with a lower energy than the first gauche structure. However this is still not the lowest energy ocnformaton possible.
From comparing the conformers of 1,5-hexadiene and their point groups in [Appendix 1]. The energies and point groups match up exactly, The anti structure above is the anti4 conformer, the gauche structure is gauche4 and the hypothesised structure is gauche2. As there are so many conformers, depending on whether the anti1 conformer was first optimised and compared the proposed hypothesis would not have been viable as this anti conformer is lower in energy thatn gauche4.
However overall it is gauche 3, with an energy of -231.69266 a.u which is the lowest energy conformation. Perhaps this is due to the anti-symmetric nature of the conformer providing the best overlap for the Gauche effect.
[[Image:gauche3.jpg|centre|200px|]]

The anti2 conformer was optimised at the HF/3-21G level of theory;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Anti2 1,5-hexadiene'''
|- align="center"
|[[Image:shanianti2.jpg|centre|300px|]] '''UPLOAD CALCULATION FILE'''
|- align="center"
|'''Energy a.u '''
|- align="center"
| -231.69254
|- align="center"
|'''Point group'''
|- align="center"
| Ci
|}

From comparing the final energies of the Anti2 configuration with Ci symmetry to that given in the appendix the energies obtained are identical at -231.69254 a.u.

After reoptimizing the Anti2 structure using the DFT method, at B3LYP/6-31G (d) level. At this higher level of theory the energy obtained was '''-234.61171 a.u''', this energy is lower in energy compared to the energy obtained from the HF/3-21G calculation. The geometry/point group remains Ci and the overall geometry did not change.

From the optimized B3LYP/6-31G* structure, the frequency calculation was computed. ppear. There were no imaginary frequencies, the IR spectrum of anti2 can be seen below.

[[Image:shaniIRanti2.jpg|centre|500px|]]

'''INSERT OUTPUT FILE'''

The following energies were obtained from the output file;
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''Type of energy'''
|'''Energy a.u'''
|- align="center"
|Sum of electronic and zero-point Energies
| -234.469176
|- align="center"
|Sum of electronic and thermal Energies
| -234.461834
|- align="center"
|Sum of electronic and thermal Enthalpies
| -234.460890
|- align="center"
|Sum of electronic and thermal Free Energies
| -234.500743
|}

The first of these is the potential energy at 0 K including the zero-point vibrational energy (E = Eelec + ZPE), the second is the energy at 298.15 K and 1 atm of pressure which includes contributions from the translational, rotational, and vibrational energy modes at this temperature (E = E + Evib + Erot + Etrans), the third contains an additional correction for RT (H = E + RT) which is particularly important when looking at dissociation reactions, and the last includes the entropic contribution to the free energy (G = H - TS).

The above energies and those obtained via the HF method have been compared below;
 

''' Summary of energies (in hartree) '''

{| border="1" cellspacing="1" cellpadding="10"
|-
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|- align="center" | '''HF/3-21G'''
|-align="center" | '''B3LYP/6-31G*'''
|- align="center" | '''B3LYP/6-31G*'''
|-align="center" | '''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'''
|-
| '''anti2 results'''
| align="center" | -231.692535
| align="center" | -231.539542
| align="center" | -231.532571
| align="center" | -234.611712
| align="center" | -234.469176
| align="center" | -234.461834
|-
| '''Literature anti2'''
| align="center" | -231.692535
| align="center" | -231.539539
| align="center" | -231.532566
| align="center" | -234.611710
| align="center" | -234.469203
| align="center" | -234.461856
|}
From comparing the values obtained to the experimental values obtained from those in the appendix it can be seen that these results are easy to reproduce only varying in the 5th decimal place however this is probably due to error and calculations only being accurate to ~1kJ/mol, 4 d.p for a.u.

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

The "chair" and "boat" transition structures for the Cope rearrangement were created below. Each consisting of two C3H5 allyl fragments positioned approximately 2.2 Å apart, one with C2h symmetry and the other with C2v symmetry.

===The "Chair" transition state===
For the chair transition state, the ally fragments were drawn as single fragments initially and optimized using the HF/3-21G level of theory. After which they were copied and pasted to create a new molgroup.

The transition state was optimised and the force constant matrix (the Hessian)was computed via method one; a TS Berny optimization.

The job was sucessful in producing only one imaginary frequency of magnitude 817.938 cm-1 corresponding to the Cope rearrangement as can be seen below.
 

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanivib817in.jpg|centre|200px|]]
|[[Image:shanivib817out.jpg|centre|200px|]]
|}

The transition state was then optimised again from a newly created transition structure using the frozen coordinate method. This time the Redundant Coord Editor was used to freeze and the length of the forming/breaking bond was specified at (2.2Å). With additional keywords Opt=ModRedundant.

From this preoptimised structure the two frozen coordinates were also optimised, using a normal guess Hessian which was modified to include the information about the two coordinates which were being differentiating along.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''TS Berny method '''
|'''Hessian method '''
|- align="center"
|[[Image:shanitsbernychair.jpg|centre|200px|]]
|[[Image:shanihessianchair.jpg|centre|200px|]]
|- align="center"
|'''Forming/Breaking bond length (Å) '''
|'''Forming/Breaking bond length (Å) '''
|- align="center"
| 2.2
| 2.2
|}

From comparing the forming/bond breaking bond lengths of that obtained from the TS Berny optimisation and the Hessian optimisation, the bond lengths for both are the same at 2.2Å, after all this would be expected as they were specified to be that length in the Hessian method and they were fixed in the TS Berny method, this suggests that the first guess structure was a good approximation.

===The "Boat" Transition state===

The Boat transition structure was optimised using the QST2 method. Where the reactants and products for a reaction were specified and the calculation interpolated between the two structures to try to find the transition state between them. The numbering of the 1,5-hexadiene product and reactants were manually changed.

[[Image:shaniboatfail.jpg|centre|250px|]]

After submitting the calculation, initially the job failed as it looked a bit like a more dissociated version of the chair transition state. The original input file was then modified so that the reactant and product geometries looked closer to the boat transition structure.

[[Image:shaniboatqst2.jpg|centre|300px|]]

The job was sucessful, it had converged, producing only one imaginary frequency at -839.717cm-1 is seen, with the following motion displayed below;

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shaniboatqvib1n.jpg|centre|200px|]]
|[[Image:shaniboatqvibout.jpg|centre|200px|]]
|}

This exercise demonstrates that although the QST2 method has some advantages because it is fully automated, it can still often fail if the reactants and products are not close to the transition structure.

===Intrinsic Reation coordinate method===

The IRC method follows the minimum energy path from a transition structure down to its local minimum on a potential energy surface.
A series of points are created by taking small geometry steps in the direction where the gradient or slope of the energy surface is steepest. The force constants were calculated once,

This takes a transition structure as its input, and finds the maximum energy along a specified reaction path, taking into account zero-point energy etc., and produces all the quantities needed for a variational transition state theory calculation. We will leave this unchecked for the purposes of this exercise.) The final option to consider is the number of points along the IRC. The default is 6 but this is normally never enough. Let's change this to 50 and see how the calculation progresses. Change the name of the chk file under Link 0 and submit the job.

When the IRC calculation has finished, open the chk file with all the intermediate geometries and see how the calculation has progressed. You will find that it hasn't reached a minimum geometry yet. This leaves you three options: (i) you can take the last point on the IRC and run a normal minimization; (ii) you can restart the IRC and specify a larger number of points until it reaches a minimum; (iii) you can redo the IRC specifying that you want to compute the force constants at every step. There are advantages and disadvantages to each of these approaches. Approach (i) is the fastest, but if you are not close enough to a local minimum, you may end up in the wrong minimum. Approach (ii) is more reliable but if too many points are needed, then you can also veer off in the wrong direction after a while and end up at the wrong structure. Approach (iii) is the most reliable but also the most expensive and is not always feasible for large systems. You can try any or all of these approaches and see which conformation you end up in.

 

{|align="center" border="1" cellpadding="5"
|- align="center"
|'''IRC, 50 points'''
|'''IRC, 400 points '''
|- align="center"
|[[Image:shaniirc400points(II)molecule.jpg|centre|200px|]]
|[[Image:shaniirc40points(II)molecule.jpg|centre|200px|]]
|- align="center"
|[[Image:shaniircmethod(II)50.jpg|centre|500px|]]
|[[Image:shaniirc400points(II).jpg|centre|500px|]]
|}

(g) Finally we need to calculate the activation energies for our reaction via both transition structures. To do this we will need to reoptimize the chair and boat transition structures using the B3LYP/6-31G* level of theory and to carry out frequency calculations. You can start from the HF/3-21G optimized structures. Once the calculations have converged, compare both the geometries and the difference in energies between the reactants and transition states at the two levels of theory. What you should find is that the geometries are reasonably similar, but the energy differences are markedly different. As a consequence of this, it is often more computational efficient to map the potential energy surface using the low level of theory first and then to reoptimize at the higher level as we have done in this exercise.

The experimental activation energies are 33.5 ± 0.5 kcal/mol via the chair transition structure and 44.7 ± 2.0 kcal/mol via the boat transition structure at 0 K. If you take the values computed at 0 K, how close are they to the experimental values? You can also find the energies with thermal correction at 298.15 K under the Thermochemistry data in the output file. If you have time, you can recompute them at higher temperature. Alternatively, you can use the utility program FreqChk to obtain energies at a different temperature. This only requires the chk file from a frequency calculation and allows you to retrieve frequency and thermochemistry data as well as calculating them with an alternate temperature, pressure, scale factor, and/or isotope substitutions. The FreqChk utility program can be accessed from Gaussian03W. Launch Gaussian03W. Select utilities from the menu and click on FreqChk to launch the utility program. You will be prompted for a chk file. Select your chk file from the C:\G03W\Scratch directory and follow the instructions from this web link to proceed.

'''BOAT TS

Perhaps the optimisation calculations did not work as the guess structures for the transition structure is far from the exact structure, thus the this approach may not have worked as the curvature of the surface may be significantly different at points far removed from the transition structure.'''

==The Diels Alder cycloaddition ==
Using the AM1 semi-empirical molecular orbital method to start with the geometry of cis butadiene was optimized. The HOMO and LUMO of cis butadiene were ten plotted and its symmetry was determined; Point group is C2v
(symmetric or anti-symmetric) with respect to plane.

First optimised using semi empirical AM1 method;
{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadiene.jpg|centre|400px|]]
|}

LUMO
Lumo is symmetric through C1 plane
HOMO
Homo is anti-symmetric through C1 plane

{|align="center" border="1" cellpadding="5"
|- align="center"
|[[Image:shanibutadienelumo.jpg|centre|400px|]]
|[[Image:shanibutadienehomo.jpg|centre|400px|]]
|}