Rep:Mod:CNLXXX

Y3C Transition States and Reactivity

Introduction

In this report, Gaussian was used to run the optimisations at both the PM6 level or the higher order B3LYP/6-31G(d) level in order to explore the competing pathways involved in a range of pericyclic reactions.

A potential energy surface (PES) describes the energy of a molecule as a function of its geometry. It is a mathematical function which can take on three dimensions, and it only depends on the relative positions of atoms or molecules to each other, rather than their absolute locations. This report contains PES plots, specifically the intrinsic reaction coordinate (IRC) which follows the PES at its minimum energy pathway throughout a chemical reaction. A minimum in the PES is a point at the bottom of a potential valley, from which motion in any direction leads to a higher resultant energy. Minimums correspond to different molecular geometries and thus by following the IRC of a reaction, you can go from one geometry (reactants) to another (products) along the PES. At minima and saddle points the gradient is zero, and so is the first derivative of the potential energy, thus meaning the force at these points is zero too due to force being the negative of the first derivative. The aim of the optimisations in this report were to find stationary points along the PES which corresponded to geometries of the respective transition states that were to be located. The curvature (second derivative of the energy) corresponds to either a minima, maxima (i.e. a transition state) or saddle point, and optimisations in computational chemistry can determine which of these it is via a frequency calculation. The number of imaginary frequencies (negative frequencies) indicates the stationary point to which the molecular geometry corresponds to: a molecule with n imaginary frequencies is an nth order saddle point meaning the minimum will have zero imaginary frequencies, and an ordinary transition structure will have one imaginary frequency since it is a first order saddle point.

Nf710 (talk) 11:07, 24 February 2017 (UTC) You have confused yourself a bit here. Just describe it in terms of second derivatives to keep it simple and you have loosely described a TS and a minimum. and nth order saddle point has n imaginary frequencies. also Guassian changes the cartesian basis into the normal mode basis where each of the modes is not couples so energy cannot be passes between them

Exercise 1 - Reaction of Butadiene with Ethene

In this reaction, the molecules butadiene and ethene were both optimised at the PM6 level, before the TS and then products were also optimised. This reaction is a [4+2] Diels Alder cycloaddition and leads to cyclohexane as a product. The reaction scheme is shown below

Cycloaddition of ethene and butadiene

The MO diagram for the formation of the TS is constructed below. Comparing this with the Jmol objects below it, we can see that there are four main orbitals that interact to form the TS MO's. These are the HOMO, LUMO, and two orbitals closest in energy to these, respectively labelled HOMO-1 AND LUMO+1.

MO diagram for formation of TS

(Fv611 (talk) 11:41, 24 February 2017 (UTC) The drawing of the TS MOs is quite unclear, but as it isn't wrong no marks were deducted)

Ethene MOs	Butadiene MOs	Transition state MO's
HOMO	HOMO	HOMO	LUMO
LUMO	LUMO	HOMO-1	LUMO+1

As can be seen in the MO diagram above, the HOMO of butadiene interacts with the LUMO of ethene as both are asymmetric, and the LUMO of butadiene inteacts with the HOMO of ethene as both are symmetric. Thus only orbitals of the same symmetry are allowed to mix to form new MO's with an overlap integral defined as

$S_{AB}=\int {\psi }_A^{*}{\psi }_{B}dV$

where ${\psi }_A^{*}$ is the wavefunction of atom A and ${\psi }_B$ is that of atom B. The integral is only non-zero when both wavefunctions are of the same symmetry, i.e. asymmetric (a) and asymmetric, or symmetric (s) and symmetric. If the wavefunctions are of opposite symmetry then the integral will be equal to zero and there will be no mixing of the orbitals.

(Fv611 (talk) 11:41, 24 February 2017 (UTC) This discussion is also a bit unclear - it almost sounds as if the orbital overlap requirements come from the symmetry ones.)

Bond Length Measurements

[4+2] cycloaddition of butadiene and ethene

The bond lengths in the two reactants and the TS were measured computationally and put in the table below. For reference, typical sp(3)-sp(3), sp(3)-sp(2) and sp(2)-sp(2) bond lengths are 1.54 Å, 1.50 Å and 1.33 Å respectively.

Bond	Bond Length (Å)
	Reactants	Transition State	Product
C1-C2	1.32731	1.38177	1.54076
C2-C3	-	2.11512	1.54003
C3-C4	1.33530	1.37974	1.50034
C4-C5	1.46835	1.41110	1.33736
C5-C6	1.33530	1.37982	1.50034
C6-C1	-	2.11437	1.54004

As can be seen from the table, the bond lengths of C1-C2, C3-C4 and C5-C6 increase from reactants to products as the double bonds in the reactants change to single bonds. From the TS to the final product cyclohexene, we can see that the bond lengths of C2-C3 and C6-C1 decrease to be about 1.54 Å, which is consistent with a single C-C bond length. The final 6 bond lengths in the product compare very well to typical bond lengths listed above. The Van der Waal radius of a typical C atom is 1.70 Å , therefore since the length of the two partly formed C-C bonds in the TS (C2-C3 and C6-C1) is 2.1 Å, which is smaller than the combined Van der Waal radii of two C atoms, the reaction is concerted and the two bonds form at the same stage in the reaction.

Vibrational Visualisation

The vibration below corresponds to the reaction path at the TS. It can be concluded from this visualisation that the formation of the two bonds in synchronous i.e. at the same time as each other.

Vibration corresponding to reaction path at TS

Exercise 2 - Reaction of Cyclohexadiene and 1,3-Dioxole

This [4+2] cycloaddition can lead to the formation of two stereoisomers - the exo or endo product, because there are two possible conformations where the hydrogens on 1,3-Dioxole are cis in the final product. The relative proportion of each isomer formed in the reaction relies on the stability of the transition state leading to the final product, as well as reaction conditions. The oxygen atoms of the dienophile are electron donating and will have some effect on the energy of the transition state, relative to that of a dienophile without heteroatoms, but there are also likely to be secondary orbital interactions between the orbitals on oxygen and the diene which stabilise one transition state more than the other.

Reaction 2 scheme

MO Diagrams

The MO diagrams below shows the orbitals which interact to form both TS's respectively. a and s refer to the MO being either asymmetrical or symmetrical. Both diagrams look similar, with the same frontier orbitals interacting, however the relative energies of each MO in the transition state is different. By running a single point energy calculation, information on the relative energies of each MO was gathered. This showed that the HOMO of the dieneophile was in fact closer in energy to the LUMO of the diene hence we would expect a greater orbital overlap integral, and hence mixing to a larger extent. This indicates that the reaction is an inverse electron demand Diels-Alder reaction, as if it wasn't, then the HOMO of the diene would mix most strongly with the LUMO of the dienophile.

MO Diagram	MO Diagram
Exo	Endo
Exo Transition State	Endo Transition State

(The order of orbitals in the MO diagram above is different to those below. Should be A-S-S-A Tam10 (talk) 13:53, 20 February 2017 (UTC))

MO Calculations and Jmols

The table below shows the MO's which interact to form the respective TS's. These are the orbitals near the HOMO and LUMO levels.

TS	Molecular Orbital
	HOMO -1	HOMO	LUMO	LUMO +1
Exo	HOMO -1	HOMO	LUMO	LUMO +1
Endo	HOMO -1	HOMO	LUMO	LUMO +1

Energies in Reactions

The table below shows the energies of activation of each of the transition states, respectively. This information was extracted from the .log output file in the "thermochemistry" section of the reactants, transition states and products.

	Energies (kJ/mol)
	Exo TS	Endo TS
Ea	166.3029563	158.4660316
ΔG	-65.0013542	-71.9882576

Reaction Scheme

As seen in the table and energy profile above, the endo TS requires a smaller activation energy of 158 KJ/mol as opposed to 166 KJ/mol to get to get to the exo TS. This is due to secondary orbital interactions (non-bonding) being present in the endo-TS which lowers its energy (i.e. lower activation energy) and favours faster formation of the endo-product. The secondary orbital interaction is between orbitals on the two oxygen atoms of the 1,3-dioxole molecule and those on the cyclohexadienyl ring. This is shown in the jmol below, by setting the mo cutoff to 0.01. The endo-product was calculated to be the thermodynamically more stable product too, as seen by the more negative free energy difference. This goes against the Alder rule stating that the thermodynamic product is the exo product, however the energy of the product is a balance between sterics (favourable in the exo case) and also on stabilising stereoelectronic interactions which are likely to be the overriding factor in the endo case. This reasoning is backed up in a study by Tormena et. al. The exo transition state doesn't benefit from this secondary orbital overlap.

HOMO showing secondary orbital interaction in endo TS

(This isn't the correct orbital Tam10 (talk) 13:53, 20 February 2017 (UTC))

Nf710 (talk) 11:17, 24 February 2017 (UTC) You haven't really explained the SSO and you haven't shown the correct orbital to show the pi interaction. Other than that your energies look good and you have come to the correct conclusion

Exercise 3 - Diels-Alder vs Cheletropic Reaction

The cycloaddition of o-Xylylene to SO2 can go either via a Diels-Alder reaction or a cheletropic one in which two bonds are simultaneously formed to the same sulfur atom. In this part, we explore the transition states leading to each of the products, and the relative energies of these transition states.

Below is a reaction scheme.

Reaction 3 Scheme

Optimisation and Visualisation

The TS's were calculated by starting with the product and working backwards, and optimising using to the PM6 level. The IRC plots as well as GIFs have been included to illustrate the mode of reaction, from reactants at infinite separation, to the final products. It can be seen that along the reaction coordinate, the unstable xylylene reactant begins to afford aromaticity at the TS until the final product is formed, which in every of the three cases is aromatic. This is undoubtedly a driving force in the reaction due the stability of aromatic systems.

Reaction pathway	IRC gif movie	IRC Graph
Cheletropic
Endo Diels-Alder
Exo Diels-Alder

Energies of the Reactions

From the table below, it can be seen that the largest activation barrier is that of the cheletropic TS formation at 260 KJ/mol. The exo TS once again requires a greater activation energy compared with the endo TS, however in this case, the exo product is in fact the thermodynamic product of the two with a more negative free energy change of reaction: -172 KJ/mol. From the three, the cheletropic product is certainly the thermodynamic one, however a higher relative temperature would be required to access it. The most favourable product is likely to be the kinetic endo-product due to its relatively low energy barrier. Below is a reaction profile which illustrates the concept more clearly. Note that the reactants are assumed to be at the zero energy level when infinitely apart.

Reaction 3 Energy Profile

	Energy (kJ/mol)
	Exo	Endo	Cheletropic
Activation Energy (Ea)	241.7422179	236.4782199	260.0808844
Free Energy Change of reaction (ΔG)	-172.1908103	-168.4238356	-231.4465991

(How were these energies derived? The barriers look far too high Tam10 (talk) 13:53, 20 February 2017 (UTC))

Conclusion

Three exercises were undertaken to locate transition structures for a range of pericyclic reactions. The computational chemistry used allowed us to explore the shapes and relative energies of the molecular orbitals which were involved in the reactions, but also to obtain thermodynamic data, hence allowing predictions to be made on the most likely products from competing pathways. Reactions could be characterised as being under kinetic control, such as o-Xylylene reacting with SO2, or reverse electron demand as when cyclohexadiene and 1,3-Dioxole combined. The latter reaction also went against Alder's rule in the sense of the endo product also being the thermodynamically more stable one, due to secondary orbital interactions with the oxygen atoms of dioxole. Visualisation of the Diels-Alder reaction in exercise 1 allowed us to determine that the process was concerted and that the two new sigma bonds formed simultaneously. The same synchronousness could be said for the three pathways in exercise three including the cheletropic mechanism whereby two new sigma bonds were formed to one sulphur atom to form the thermodynamic product.