Mini Paper: Orbital Symmetry Rules for Unimolecular Reactions

Ralph G. Pearson, JACS, 94:24. 1972

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To predict the course of a reaction Perturbation theory has been applied rigorously, here the author

has come up with simple symmetry rules, which accounted for several unimolecular reactions shown

here.

To start, The Transition density: changed electron density for the mixing of ground and excited state

wave function in the course of reaction, ρ, is proportional to Фi x Фf where Фi is initial and Фf is final

MO occupied. So reaction path will be chosen by the reactant(s) in where the symmetry of the

reaction coordinate will be same as the Фi x Фf. After reaction begins Q must be totally symmetric.

For Unimolecular reactions this has been discussed as follows:

H2 → 2H

The valence shell orbitals are of σ g (b.) and σu (a. b.) symmetry. The reaction coordinate is totally

symmetric, or Σg+. Dissociation must involve movement of electrons from the σ g to σ u orbitals. The

symmetry rule then requires that the excited state which mixes into the ground state is the doubly

excited configuration, (σ u)2.

CH4 → CH3 + H

Requires a Tz vibration to break the Td point group. This can occur most easily by a (t2) → (a1*)

excitation. After a short extension of the carbon-hydrogen bond, the point group becomes C3v , the

reaction coordinate becomes A1, and the remaining process is that for a heteronuclear diatomic

molecule.

SF4 → SF2 + F2 -allowed

SO2F2 → SO2 + F2 -forbidden

The S-F bonds to be broken in both cases are of a1 and b2, symmetry in the C2v point group. The F-F

bond to be made is of a1 symmetry. In the case of SF4, the remaining new bonds are actually

antibonding, since a π* orbital of b2 symmetry is filled.

In the case of SO2, which has two fewer electrons that SF2, the new orbital that is filled is either an

antibonding σ * orbital of al symmetry, or a π nonbonding MO of a2 symmetry. These two orbitals

appear to have rather similar energies. At any rate, normally there are no electrons in the higher

energy π* orbital of b2, symmetry. Since under the influence of an A1 perturbation (the changing

reaction coordinate), electrons cannot move from a b2, orbital (S-F bonding) into either an a1* or a2*

orbital. The symmetries of the bonds and the reaction coordinate do not match up. Hence the

reaction is forbidden.

C6H10 → C4H6 + C2H4

the bonds that are broken (the 3-4 π bond and the 1-2 and 5-6 σ bonds) are of 2A’ + A” symmetry.

The bonds to be made (the 1-6, 4-5, and 2-3 π bonds) are of the same symmetry.

They concluded, the rule that a reaction is allowed, if the symmetries of the bonds that are made

match up with the symmetries of the bonds that are broken.

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-Sujoy Saha

BS-MS

20101095