Rep:Mod3:llama2822
Computational Labs Module 3; Physical Chemistry
Introduction
This page documents the experiments carried out between the 18th to the 26th March on the third year computational labs module three. This module comprises of the physical aspect of the computational labs course and will revolve around one exercise, that of the cope rearrangement. Each step will comprise of three segments, a discussion; regarding various inferences obtained from the results and potentially highlights possible reasons, a results section which encompasses the resultant data from the calculations in the form of tables and graphs, and finally an experimental section which covers the method of the respective calculation.
The Cope Rearrangement
The cope rearrangement is a [3,3] sigmatropic reaction which is a form of pericyclic reaction. Due to it being a pericyclic reaction there is only one concerted step, meaning no intermediates and only one transition state. In this reaction the transition state involves one sigma bond being broken and one being formed. There is no nucleophilic or electrophilic component of the reaction, being that the flow of electrons can happen either clockwise or anticlockwise and additionally the reaction is promoted by either light of thermal energy.
This exercise will look at the classic Cope rearrangement of the symmetric 1,5-hexadiene which unlike most studied rearrangements is completely reversible due to the high symmetry. This rearrangement can occur via two pathways due to its six membered ring state, which is that of the chair or boat transition states. The initial molecule will be modelled in various conformations and compared and then the experiment will move onto optimising the chair and boat transition structures in a number of ways for both.
Conformations of 1,5-hexadiene
Discussion
% Memory Limit Variations
An initial conformation of 1,5-hexadiene was drawn in an anti arrangement of the central four carbons and run through Gaussian with the %mem at 250 and 500MB. The difference between the two runs was negligible (figure 1), with geometries of the molecule almost identical (C1-C6 carbon distance of 5.9358 and 5.9357 Angstroms) and the energies differ only by one millionth, and the time for the calculations to run were identical (1m 33s). The gradients of the calculations differed slightly with the larger memory percentile calculation being slightly higher (2E-05) which is counterintuitive as possibly more memory used would lead to a more intricate and higher resolution calculation however this is not the case. Ultimately for these small, simple molecules a change in the percentile memory limit is not mirrored in the final result.
Anti and Gauche conformations
From this anti (2) conformation, the molecule was adapted to a gauche linkage. This is generally considered to be more stable than expected, due to the better donor of the sigma CH bond into the antibonding sigma CC orbital, in light of the higher interactions between the chain groups[1]. From analysis of the conformation energies (Table 1) it shows that the Gauche 3 conformation is actually the most stable, however due to the various orientations of the other groups, it does not show an exact trend. Because these allyl groups are small the steric interaction between the two carbon carbon bonds in the gauche conformation is minimised, therefore the stereo electronic interaction can be said to predominate giving slightly more stable gauche conformations.
As shown in the relative energies the Gauche 1 conformation is the highest with the double bond groups interacting strongly with each other, and the anti 3 double bonds position themselves between the two hydrogens connected to the opposite sp3 carbon in the chain. However these hydrogens still interact strongly with each other which gives rise to the high energy.
Results
| Conformation | Jmol | Image | Point Group | Gradient of calculation/a.u. | Calculated Energy/a.u. | Energy/kcalmol-1 | Relative Energy |
| Gauche 3 | 
|
C1 | 0.0000086 | -231.69266 | -145389.22938 | 0.00000 | |
| Anti 1 | 
|
C2 | 0.00001467 | -231.69260 | -145389.19173 | 0.03765 | |
| Anti 2 | File:Llama303.jpg | Ci | 0.00003901 | -231.69254 | -145389.15408 | 0.07530 | |
| Gauche 4 | 
|
C2 | 0.00002105 | -231.69153 | -145388.52030 | 0.70909 | |
| Anti 4 | 
|
C1 | 0.00000969 | -231.69097 | -145388.16889 | 1.06049 | |
| Anti 3 | 
|
C2h | 0.00000509 | -231.68907 | -145386.97663 | 2.25276 | |
| Gauche 1 | File:Llama307.jpg | C2 | 0.00001949 | -231.68772 | -145386.12949 | 3.09989 |
Table 1; Showing the different conformations of 1,5-hexadiene
Experimental
The molecule 1,5-hexadiene was drawn in gaussview and an anti periplanar conformation was drawn and cleaned up in gaussview. From this the structure was optimised using the Hartree Fock 3-21G method with the memory limit set to 250 MB and the calculation was run. The checkpoint file was opened and an image taken of the molecule and also the energy and gradient that the calculation determined were recorded. The symmetry was made note of and the optimised molecule was then changed to various conformations of both gauche and anti types.
Method and Frequency Analysis of Anti 2 conformation
Comparison of calculation methods
The two methods are the Hartree Fock 3-21G and the DFT B3LYP method and pseudo potential. These were both used to calculate the optimisation of the anti 2 conformation and the results given were similar, with the DFT B3LYP method being slightly deeper in energy (Table 2). By looking at both optimised molecules, both of them kept their allylic bonds parallel to each other, however the sp3 carbon bond angles are slightly larger in the B3LYP optimised molecule (111.4o compared to 112.7o), resulting in a longer molecule of 6.019 Angstroms (cf. 5.936 Angstroms for the HF optimised molecule).
One possible explanation is that the DFT method has a higher basis set (6-31G) than the 3-21G set meaning that higher order orbitals are more accurately defined. This allows it to make better approximations of higher row elements in calculations. However this is not of concern due to the deep in energy carbon and hydrogen atoms. Another explanation is that the hartree fock method’s reliability breaks down after only 3 atoms, therefore certain interactions which would decrease the bond lengths within the molecule would not be considered, giving a higher in energy and longer molecule.
Results
| Method | Total Energy/a.u. | Energy Gradient/ a.u. | Point Group | Image |
|---|---|---|---|---|
| HF/3-21G | -231.6925 | 0.00001933 | Ci | File:Llama312.jpg |
| DFT B3LYP 6-31G* | -234.6117 | 0.00001325 | Ci | 
|
Table 2; Showing the Variance of methods with the Anti 2 conformation
| Value | Meaning | HF 3-21G | DFT B3LYP |
| Sum Electronic & Zero Point Energies/a.u. | Potential Energy at 0K | -231.5395 | -234.4692 |
| Sum Electronic and Thermal Energies/a.u. | Enerygy at rtp | -231.5326 | -234.4619 |
| Sum Electronic and Thermal Enthalpies/a.u. | Energy at rtp plus RT term | -231.5316 | -234.4609 |
| Sum Electronic and Thermal Free Energies/a.u. | Entropic Contribution | -231.5909 | -234.5008 |
Table 3; Showing the Thermochemistry energies of the Anti 2 conformation with different energies
Experimental
The anti 2 molecule was reoptimised by using the B3LYP/6-31G (d,) level under the DFT method. The energies of the two methods were compared and their geometries compared. From this a frequency calculation was run using the B3LYP level. This frequency calculation returned a full vibration spectrum as shown in the results section. No imaginary vibrations were returned. Through looking at the output stream, the thermochemistry section was found where various energies were shown.
Chair and Boat Transition states
Discussion
Chair Transition State
The chair transition state was modelled two ways, first via an optimisation and frequency calculation from the initial guess shown in Figure 3, using TS (Berny) giving one imaginary frequency of 817.92cm-1.
In addition to this calculation, the Redundant Coordinate Editor was used to fix the initial guess shown in figure 3 to 2.2 Angstroms and the optimisation calculation run. However when the second calculation was run, whilst changing the bonds concerned to unidentified, a number of times the result yielded structures shown in Figure 5. Eventually a result was returned that looked reasonable and the resultant stretch of -817.98cm-1, slightly higher in energy than the previous method, however due to accuracy, frequencies can only be quoted to 0 decimal places, effectively making them equal and showing the methods do not deviative from each other in frequency calculations. This can also be said for the total energy, which is also of exactly the same energy for both molecules.
| Method | TS (Berny) | Redundant Coordinate Editor |
|---|---|---|
| Imaginary Vibration |  |
File:Llama324.JPG |
| Frequency/cm-1 | -817.98 | -817.92 |
| Total Energy/hartree | -231.61932 | -231.61932 |
Table 4; The variation of energies with altering methods
Initially the first tries with the hessian derivatives yielded a result such as the structure in figure 3. This resulted in one side of the fragments being very close together at 1.01 angstroms and the other side far away from the 2.2 Angstroms specified. This was due to the force constants being left on and for some reason created a result such as the one shown. Table 4 shows the variance between methods for the transition state are negligible and result in both the same energies and frequencies of vibration.
Boat Transition State
Initially using the QST2 method, the calculation did not complete, and resulted in a structure like that in Figure 5. From this it was clear that the geometries of the anti conformation was not close to the actual boat transition state and had to be adapted to a 0o dihedral angle of the central four atoms and a bond angle of the sp3 carbons of 100o to result in the two double bonds coming closer together.
From this a refined QST2 calculation was run and this yielded a reasonable structure
For the boat transition state the calculation returned an energy of -231.60280 hartree with one imaginary vibrations of -840.80cm-1 which is shown in Figure 6.
QST 3 Method
Moving on from the QST 2 calculations QST 3 concerns three input structures, the initial two used in the previous calculation and the final transition state result yielded from it. The three input structures are shown above (figure 7). However the same problem which had arisen in the previous calculation ensued, the geometries of the reactants and products.
As with the previous example, the geometries of the reactants and products were modified to mimic that of the transition state. The third run consisted of a dihedral angle of 85o and sp3 C=C-C bond angle of 121o
Results
| Transition State | Chair Transition State | Boat Transition State |
|---|---|---|
| Image | |
|
| Total Energy/a.u. | -231.61932 | -231.60280132 |
| Sum of Electronic and Zero-point Energies/a.u. | -231.46670 | -231.45092 |
| Sum of electronic and Thermal Energies/a.u. | -231.46134 | -231.44528 |
| Sum of electronic and Thermal Enthalpies/a.u. | -231.46040 | -231.44434 |
| Sum of electronic and Thermal Free Energies/a.u. | -231.49521 | -231.47912 |
| Imaginary Vibration/cm-1 | -817.98 | -840.80 |
Table 5; Showing the variance in energies of the chair and boat transition states
Experimental
A CH2CHCH2 fragment was drawn with delocalised bonds and this was optimised using the HF/3-21G method and set. The geometry optimised fragment was then added to a new molecule group twice (append molecule) and moved around with respect to the other fragment to give a chair like transition state with the fragments 2.2 Angstroms apart by their terminal carbons. A calculation was run regarding the optimisation and frequency, with optimisation to a TS Berny. Opt=NoEigen was added to the additional notes, and the calculation of force constants were set to run once. The calculation returned a transition state with one imaginary frequency of -817.92cm-1.
In light of this calculation, a different method was used by using the original transition state group and the redundant coordinate editor fixed with the two sigma forming/breaking bonds being classified as bonds and frozen at 2.2 Angstroms. This molecule was then optimised and the coordinate editor reopened and the bonds set to derivative. The optimization was run without the force constants being calculated and this Hessian modified result first yielded a transition state with two of the terminal carbons close together and the other end far away. Another couple of runs resulted in similar structures. A calculation eventually returned an optimised structure.
Moving onto the boat transition state structure the anti 2 B3LYP optimised molecule was opened and added to a new molecule group. A new group was added to that yielded two windows, where a second molecule was added. The atoms were re numbered to mirror the products and reactants of the cope reaction. Then the two molecules were optimised using the optimisation and frequency method with TS (QST 2) selected. This calculation fails to yield a distorted chair so to rectify this, the geometries of the molecules were adapted to mirror the transition state, with the C2-C3-C4-C5 dihedral angle being changed to 0o and the bond angles of the C2-C3-C4 and C3-C4-C5 carbons changed to 100o. This was run under the same criteria and yielded a reasonable result of a boat transition state, with one imaginary vibration of -840.8cm-1.
From this the resultant transition state was added into the start of the two molecules and the QST 3 method was used to try and determine a more refined value. Three runs were tried by varying the dihedral angles and bond angles discussed previously to 65 & 150 (ii) and 85 & 121 (iii). These three calculations are shown in the results section.
Chair IRC Calculation
Discussion
IRC Calculation
The first IRC calculation yielded a structure which didn't have minimum geometry. This was due to the low number of steps specified, this problem is shown in figure 11 where the gradient is non zero resulting in no minimum.
Three techniques were used to rectify this, with only one working which was to take the last optimised segment in the previous calculation and forward that for another IRC optimisation. 25 more steps were run to give a more accurate stationary point with it's lowest energy being -231.69145137 hartree, compared to the original run of -231.68328049 a difference in real terms of 5.12kcalmol-1. As shown by the graph in figure 12 the energy still hasn't reached a low point, but has a much lower gradient than the previous calculation.DOI:10042/to-4801
Variance of Bond Length with optimising geometry
It is interesting of note how the program runs the calculation with respect to the forming bond lengths. Pericyclic reactions in their nature are completely concerted and the bond breaking and forming happen at the same time. However by looking at the IRC calculation and each step within it, it shows that in the calculation, some bonds are formed earlier than others.
By looking at figure 13 it is clear in the geometry optimisation that the C2-C1 bond (that of the sigma bond to pi bond) occurs the fastest, most probably as the electrons are moved into the anti bonding orbitals of this bond to break the other bond. The forming C3-C11 sigma bond occurs at a steep gradient as it is being formed through space and these are highly favourable interactions, however it takes a certain time to equilibrate to it's resting length. The C2-C3 bond increases it's bond length by transforming from the allyl bond to it's alkyl derivative.
What is also of note is the equal weighting of the C2-C1 bond and the C3-C11 bond at 1.38 Angstroms. This is due to the fragments being used, which are in their equilibrium position with the electrons moving between both bonds, therefore they are delocalised and the bond lengths are equal.
Experimental
The checkpoint file of one of the optimised chair calculations was opened and the IRC job type was selected. The calculation was run in only one direction, the force constants only calculated at the start and the number of steps were set to fifty. The calculation returned an unoptimised transition state, so the three methods to re-optimise the structure were carried out, with only one returning a results. The 23rd step of the first calculation was resubmitted under the same conditions, and yielded a further 25 steps, which were added onto the original number. This showed a flattening curve meaning that the calculation was going to the same minimum point as the previous one.
B3LYP determination of activation energy
Discussion
The use of the B3LYP method returned lower energy results, as shown in the previous comparison with the Anti 2 conformation, and in comparison to the HF methods for the transition states, again the chair state is deeper in energy. However it is shown that the imaginary frequency for the B3LYP chair calculation is more negative, i.e. weaker in energy compared to the boat transition state. Originally in the HF method it was the boat with a more negative imaginary vibration. This may possibly be due to the varied methods used to obtain the HF results. However it shows a general trend that the chair transition state is more stable than the boat. This is shown explicitly in table 8 where the energies are shown in kcal/mol-1.
The energies for the B3LYP method show exactly the same trend as the HF method, with the chair transition state having a lower difference in energy with respect to the anti 2 conformation and therefore the more favoured compared to the higher energy boat transition state. However the B3LYP methods show a smaller variation between the chair and boat energies being 7.87 and 8.13kcal/mol-1 compared with 9.9 and 10.07kcal/mol-1 for the HF method. These are for the activation energies at 0K and 298.15K respectively.
By looking at the calculated experimental values for the two transition states, it shows that the B3LYP are of a better comparison than the HF methods. However the chair transition state is slightly higher than the experimental value and the boat slightly lower. The HF method for both transition states result in a much higher activation energy compared to the experimental value.
Results
| Transition State | Chair | Boat |
|---|---|---|
| DOI | DOI:10042/to-4805 | DOI:10042/to-4789 |
| Image of Vibration |  |
|
| Frequency/ cm-1 | -569.17 | -530.17 |
| Total Energy | -234.55693 | -234.54309 |
| Sum of electronic and zero-point energies | -234.41488 | -234.40234 |
| Sum of electronic and thermal Energies | -234.40895 | -234.39601 |
| Sum of electronic and thermal Enthalpies | -234.40801 | -234.39506 |
| Sum of electronic and thermal Free Energies | -234.44312 | -234.43110 |
Table 6; Results of the B3LYP 6-31G* transition states
| Method | HF 3-21G | HF 3-21G | DFT B3LYP | DFT B3LYP | Experimental |
|---|---|---|---|---|---|
| Temperautre | 0K | 298.15K | OK | 298.15K | OK |
| Chair delta E/kcalmol-1 | 45.68 | 44.69 | 34.09 | 33.19 | 33.5 +/- 0.5 |
| Boat delta E/kcalmol-1 | 55.58 | 54.76 | 41.96 | 41.32 | 44.7 +/- 2.0 |
Table 7; Activation Energies of the chair and boat transition states
Experimental
Using the previous HF optimised chair and boat transition state structures, both were set under an Opt+Fq calculation with a DFT B3LYP 6-31G* method which yielded the required structures under TS Berny minimisation. From this the thermochemistry data was recorded and to calculate the activation energies for the two transition states, the thermochemistry data for the anti 2 conformation of the reactant was used to calculate the difference and then the units converted to kcal/mol-1 for comparison with the experimental data. Two activations energies could be calculated, that at 0 Kelvin derived from the electronic and zero point energies, and that at 298.15K, the sum of electronic and thermal enthalpies. These gave the desired activation energies.
References
- ↑ Smith, E.; 2009.; Conformational Analysis Lectures.; Imperial College London