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 C2v point group. The HOMO and LUMO have, respectively, σ-type (A1) and π-type (B2) symmetry and are separated by about 1 eV.
Symmetric and antisymmetric combinations of these orbitals give the C-C bonding and antibonding orbitals of ethylene (ethene, C2H4). Ethene belongs to the D2h point group.
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 D3h 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.
|References||Walsh Cyclopropane home||Derivation of the MOs|
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