Structure of Cyclopropane and Ethylene Oxide

It is of interest to consider the results of applying the non-localized molecular orbital theory, as developed largely by Mulliken, Lennard-Jones and Hund, to the problem of the structures of cyclopropane and ethylene oxide, concerning which there has recently been some controversy1,2,3. The fundamental point of the theory is that any molecular orbital, which may be bonding or otherwise in all the nuclei, must conform to an irreducible representation of the point group of the nuclear skeleton. The case of the equilateral triangle, important for cyclopropane, has been touched on by Mulliken4, who shows that for any given type of orbital of X in X3 (point-group D3h) it is possible to construct two such orbitals with the following eigenfunctions: