Rep:Mod:cheesecake10

Contained within these wiki pages is the report by Martin Champion (mjc07) for the Third Year Physical Computational Project, Department of Chemistry, Imperial College London (March 2010).

The aim of this report is to show the findings of investigations into transition states for simple chemical reactions and rearrangements. The Cope rearrangement will be studied in particular

Transition state modelling of Organic systems

The aim is to investigate ways of computing transition states of simple organic reaction, looking at reaction potential energy surfaces and following a minimum path to calculate properties such as activation energies. This will be done using GuassView 5 as an interface/visualiser and Guassian 09 calculation software.

Cope Rearrangement

Fig 1: 1,5-hexadiene (Drawn in a trans/anti conformation)

File:Mjc07 cope scheme.png

The Cope rearrangement was discovered in the 1940's by Arthur C Cope and cis now known as a concerted pericylic reaction in particular a [3,3] sigmatropic rearrangement. It proceeds by sigma bond formation between the termini of a two π systems, in 1,5-hexadiene with simultaneous bond breaking at the three position and shift of the π systems. It is important to note that this is a chemical reaction, not a resonance form, and although for an unsubstituted 1,5-hexadiene the product and reactant are the same there has actually been a bond broken and a new one formed between different carbons (which would be seen if one of the C atom positions was enriched with C13). The other suggestion that it is a chemical reaction is the high temperature usually required for these change to occur.

Optimising the reactants/products

To begin modelling 1,5-hexadiene was constructed in GaussView 5. It was arranged in a trans fashion across the central butyl linkage (C2-C3-C4-C5 dihedral angle=180^o), so called anti conformation. This is equivalent to a linear chain representation in terms of the central C-C bonds. Relation of the two double bonds to this linkage was not formalised at this point. The geometry was then optimised using ground state hartree foch theory with the 3-21G basis set. This is an entry level optimisation but it is a relatively quick calculation when compared to the higher basis sets.

Table 1: First Optimised Reactant (anti)

Calculation	RMS gradient norm	Energy (Hartrees)	Point group	Conformation
HF/3-21G	0.00000260	-231.68907	C2h	anti3

This is one conformation but because there are three separate C-C single bonds in the molecule which can be rotated so there are effectively an infinite number of conformations. For the purposes of this exercise it useful to find the lowest energy conformation but also how the energy compares for geometrically important conformations such as those that might lead to a reaction. To that end the central linkage could also be arranged in a gauche way (C2-C3-C4-C5 dihedral angle=60^o).It is expected that from the conformations of Butane that this will be higher in energy because bulk of the two C-C=C groups are now much closer together (60^o vs 180^o)

Table 2: Second Optimised Reactant (gauche)

Calculation	RMS gradient norm	Energy (Hartrees)	Point group	Conformation
HF/3-21G	0.00004611	-231.68772	C2	gauche 1

Fig 3: Orbital overlap leading to eclipsed conformations on terminal alkenes

Because there are also two other dihedral angles to consider it is difficult to predict a conformation with the lowest energy. Initial guesses (leading to the first anti structure above) would have predicted that this would have the lowest energy based on conformations of Butane (and other simple aliphatic alkanes). This is where every all carbon to carbon bonds are antiperiplanar to each other so as to avoid any clashes of the sterically large parts of the chain.

However if we begin to take into account the electronic properties of the alkene portions we can begin to see that it may be favourable to have eclipsed conformations because of the orbital overlap (hyper-conjugation) described in Fig 3. This conjugation stabilises the δ⁺ carbon in alkene bond by extending the molecular orbital (or orbital overlap). The conjugation can also occur between σ_C-C bond as well as the σ_C-H shown in the diagram. To that end the C_i (which is described below as C_i conformation, See table 4+5).

On comparison with the data given in the script, it can be seen that there is a gauche conformation which is slightly more stable. This is likely because in this case it is a σ_C-H donating into the π* anti-bonding orbital of each alkene rather than σ_C-C. This indicates that σ_C-H is a better donor thus more stabilising (only slightly more in this case).

Table 3: Another anti conformation (midway between anti conformation above and below

Calculation	RMS gradient norm	Energy (Hartrees)	Point group	Conformation
HF/3-21G	0.00008679	-231.68733	Cs	-

In order to use in further calculations the C_i anti conformer was drawn and optimised at HF/3-21G level. This was then further optimised now using DFT-B3YLP with 6-31G* basis set (*=(d) polarizable). The results of the two calculations are shown below.

Table 4: C_i anti conformer calculations

Calculation	RMS gradient norm	Energy (Hartrees)
HF/3-21G	0.00004313	-231.69254
DFT-B3YLP/6-31G*	0.00006243	-234.6117

Table 5: Comparing geometry information

Calculation	C2-C3/C4-C5 bond length (A)	C3-C4 bond length (A)	C=C bond length (A)	Jmol
HF/3-21G	1.509	1.553	1.316
DFT-B3YLP/6-31G*	1.504	1.549	1.333

They key difference in the calculation is the total energy it produces for each molecule. The DFT method is using a higher basis set so is better able to approximate the atomic/molecular orbitals involved (i.e. the electronic properties) and thus predicts the structure to be more stable. The overall geometry of the molecule has not changed between calculations, same symmetry and roughly the same bond angles. There has been a small readjustment of bond lengths, with the alkene bond getting longer and subsequently the two single bonds getting shorter. This can be explained through the calculation better able to approximate electronic properties of a double bond and thus calculate a more appropriate bond length. Below is a table of key thermodynamic properties which will be used in later calculations: The first value is the total energy + a correction for the zero point vibrational energy at 0K, then a correction for thermal energy at 298.15K, then an enthalpy term correction and finally a free energy term (entropy) correction (last two both at 298.15K).

Table 6: Thermochemistry Energies from Frequency analysis (Hartrees)

Sum of Electronic + Zeropoint (0K)	Sum of Electronic + Thermal	Sum of Electronic + Thermal Enthalpies	Sum of Electronic + Thermal free energies
-234.469210	-234.461853	-234.460909	-234.500826

Optimising the Chair transition state

File:Mjc07 chairboat.png

There are two possible transition states which geometrically would allow the reactions to occur. It is apparant from the conformation in the reaction scheme and the fact that it is a pericylic reaction that it must come into a pseudo cyclic conformation before the reaction can occur. Because it is a 6 membered system this can be approximated by cyclohexane conformations of either chair or boat with one sigma bond forming and one breaking and the π system delocalised.

Table 7: Optimised Ally Fragment

Calculation	RMS gradient norm	Energy (Hartrees)	Point group
HF/3-21G	0.00008791	-115.82304	C1

To construct a chair like transition state first an allyl fragment was constructed CH2-CH-CH2 (representing the movement of π system) and optimised at HF/3-21G level. Upon completion two of the optimised fragments was positioned together in a chair like fashion (alternate directions) and the distance between the two termini set at 2.2A in the z axis. This is now a 3d representation of the chair transition state in the fig 4 above. It will be now optimised to a transition state which will begin to approximate the position of electrons at this point.

This was then optimised to a Transition state (Berny) and frequency analysis carried out at the same time. This yielded a transition state structure with a negative frequency of vibration at -818 cm^-1. This corresponded to the bond formation and bond breaking stretches which is what would be expected if the curly arrow mechanism above is correct.

Another method of computing this transition state would be to fix the co-ordinates and bond length between the two termini of allyl fragments (using Redundant co-ordinate editor), optimise in this state (Minimum), then relax this constraint and optimise the whole structure again (TS Berny). The resulting transition state was the same in both cases (same geometry and negative frequency). This method however maybe useful in fixing a portion of the guess transition state structure when exploring if there are multiple transition states (thus reaction pathways) a particular reaction could take.

Table 8: Optimised Chair Transition states using both methods

Redundant Co-ord?	Calculation	RMS gradient norm	Energy (Hartrees)	C1-C6/C3-C4 bond length A	Point group
No	HF/3-21G	0.00002266	-231.61932	2.02	C1
Yes	HF/3-21G	0.00003233	-231.61932	2.02	C1

Table 9: Thermochemistry Energies for Chair transition state

Sum of Electronic + Zeropoint (0K)	Sum of Electronic + Thermal	Sum of Electronic + Thermal Enthalpies	Sum of Electronic + Thermal free energies
-231.466700	-231.461341	-231.460397	-231.495206

Optimising the Boat transition state

A different approach was used to calculate the boat transition state. The optimised C_i conformation reactant was placed in a mol group in Gaussview and a second place in the same mol group to represent reactant and product (Fig 5). These were numbered individually to reflect the numbering in the reaction scheme (so the calculation knows where the bonds are forming/breaking). The system was then optimised to a transition state (+freq analysis) using the TS (QST2) method. This aims to try compute the transition state by comparing reactant and product geometries, where bonds and are broken and made and finding the effective mid point state (geometry between them). This calculation initially fails. The problem is that quite a large amount of rotation needs to be done before this chain conformer becomes a pseudo-cyclic conformer and reaction can occur. The calculation can only take small steps each time to rotate these bonds and thus will usually fail well in advance of actually converging on the TS and possibly missing it by rotating the bonds in a direction not leading to the TS.

Fig 5: Original Reactant/Product geometry

File:Mjc07 boatguess2.JPG

To help it along the product and reactant geometries were edited to bring the termini of chain closer together as per instruction (Fig 6). The dihedral angle between C2-C3-C4-C5 was set at 0^o and C2-C3-C4 and C3-C4-C5 bond angles were reduced to 100^o. This has the desired effect and the calculation now succeeds in producing a transition state. This is almost identical to the one above except the allyl fragments are now on top of each other and pointing the same direction. The negative vibration frequency has changed slightly and is -840 cm^-1 which would be expected given the change in geometry.

Table 9: Optimised Boat Transition state

Calculation	RMS gradient norm	Energy (Hartrees)	Point group
HF/3-21G	0.00008347	-231.60280	C2v

Table 10: Thermochemistry Energies for Boat transition state (HF/3-21G)

Sum of Electronic + Zeropoint (0K)	Sum of Electronic + Thermal	Sum of Electronic + Thermal Enthalpies	Sum of Electronic + Thermal free energies
-231.450928	-231.445299	-231.444355	-231.479120

Data for Boat Transition State attempt (HF) from react/prod in Fig 5 http://hdl.handle.net/10042/to-4844 Data for Boat Transition State (HF) from react/prod in Fig 6 http://hdl.handle.net/10042/to-4843

Following the reaction path (IRC)

It is possible to follow the reaction through a reaction path on the minimum potential energy surface to examine how the geometry changes as a reaction proceeds from the saddle point to reactant or product pathways (This reaction is symmetrical so only the forward direction will be considered). The Chair conformation transition state was sued The parameters were set at calculate Force constant once and take 50 steps.

Figure 7 shows the Energy minimisation with the above parameters and how the RMS of the graident changes as it progresses. It can be seen that the gradient is still quite far from 0 (much closer to 0.0001) and even increases in the final geometry. Thus it is unlikely the calculation has actually reached a minimum. The energy of the 26th geometry was -231.68864 (Hartrees)which is higher than those listed for the various conformations listed in the script . The 27th geometry appear to look like a transition state and the 26th had the lowest energy.

File:Mjc07 ircfail graph.JPG

File:Mjc07 irccalc graph.JPG

To increase the chances of reaching a minimum the calculation was changed to allow force constant calculation at every step. This produced the graphs in Figure 8 and did indeed reach a minimum. Again the penultimate geometry was used (final was only slightly higher in energy and was drawn as if transition state whilst penultimate was drawn as a product molecule) which was found to have the same energy as gauche2 from the script, -231.69165 Hartrees.

This conformation is only a slight deviation from transition state structure geometries which is no real surprise given that such a conformation is needed to bring the termini closer enough for reaction to occur and because the reaction is symmetrical. It is therefore quite possible that submitting this conformation into the TS (QTS2) calculation above would result it being able to find a transition state.

Data for IRC Chair transition State - http://hdl.handle.net/10042/to-4841 Data for IRC Chair transition State (Calculate FC always) http://hdl.handle.net/10042/to-4842

Activation energy

The final property calculated in this experiment was the activation energy for the reaction. This was done by comparing the thermodynamic properties of the reactant (in C_i conformation) and those of the transition state (in particular Sum of Electronic + Zeropoint for 0K E_a and Sum of Electronic + Thermal for 298.15K E_a) after re-calculating at DFT/B3YLP-6-31G level first. Table 11 and 12 below

Table 11: Thermochemistry Energies for both TS's using DFT-B3YLP/6-31G

TS	Sum of Electronic + Zeropoint (0K)	Sum of Electronic + Thermal	Sum of Electronic + Thermal Enthalpies	Sum of Electronic + Thermal free energies
Chair	-234.414917	-234.408996	-234.408052	-234.443802
Boat	-234.402342	-234.396008	-234.4395063	-234.431097
Reactant (Ci)	-234.469210	-234.461853	-234.460909	-234.500826

Table 12: Activation Energies (kcal mol^-1)

	3-21G		6-31G*
TS	ΔEa - 0K	ΔEa - 298K	ΔEa - 0K	ΔEa - 298K	ΔEa - Expt 0K
Chair	45.70	44.69	34.06	33.17	33.5 ±0.5
Boat	55.60	54.76	41.96	41.32	44.7 ±2.0 ,

It can be seen that the comparing the activation energy at 0K that is still some way off from experimental value. Both are approximately 10 kcal mol^-1 higher in energy. This could be for a variety of reasons, the transition states found may not be the true minimum energy transition state or the calculation still doest trully approximate the electronic properties enough to calculate an accurate energy. In one way it does agree with experiment is that the boat transition state is higher in energy than in the chair transition state but which state the reaction will proceed through will very much dependant on the confirmation the molecule is in.

Data for Chair TS at 6-31G level - http://hdl.handle.net/10042/to-4846

Data for Boat TS at 6-31G level - http://hdl.handle.net/10042/to-4845

Data for Reactant C_i. at 6-31G level - http://hdl.handle.net/10042/to-4851

Conclusion

In conclusion the sigmatropic of re-arrangement of 1,5-hexadiene was studied extensively at a basic level looking at ways to compute reaction transition states/pathways. Some basic reaction properties have been predicted based on this calculation and compared to the literature.If time have allowed it would have been interested to study the effect substituents on the molecules have on structure of the reactant/products and transition state geometries. This is approaches situations which are more synthetically useful where the Cope re-arrangement is utilised to produce a whole new chemical species (structural isomerism, cyclisations). Such calculations are already present such as phenyl substitued 1,5-hexadiene by S Sakai