Walsh Cyclopropane Molecular Orbitals

Background

The primary assumption of the method used by Walsh to derive the molecular orbitals of cyclopropane is that only the frontier orbitals of the component fragments interact to form new carbon-carbon bonds. It is assumed that all other orbital interactions cancel.

The frontier orbitals are the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO).

Molecular orbital energies are from Extended Hückel calculations.

A.D. Walsh developed his cyclopropane picture from a consideration of the frontier orbitals of methylene (CH₂). Methylene belongs to the C_2v point group. The HOMO and LUMO have, respectively, σ-type (A₁) and π-type (B₂) symmetry and are separated by about 1 eV.

a1	b2

Symmetric and antisymmetric combinations of these orbitals give the C-C bonding and antibonding orbitals of ethylene (ethene, C₂H₄). Ethene belongs to the D_2h point group.

b1u	b3g
ag	b2u

Walsh originally proposed his cyclopropane picture as a way of explaining the properties of ethylene oxide (oxirane). He considered the effect on the molecular orbitals of ethene (as shown above) of the approach of an atom of oxygen, and proposed that oxirane III be considered as the "coordination compound" I.

He immediately saw that cyclopropane IV could also be considered in this way (II). However, the D_3h symmetry of the molecule, in which all carbon atoms are equivalent, forbids considering cyclopropane formally as a perturbation of ethylene by methylene. Instead, three equivalent methylene units would be used, with the frontier orbitals combining to form the cyclopropane ring.

Copyright © 1997 by Daniel J. Berger. This work may be copied without limit if its use is to be for non-profit educational purposes. Such copies may be by any method, present or future. The author requests only that this statement accompany all such copies. All rights to publication for profit are retained by the author.