Chemical bonds and complex wavefunctions

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Abstract
A study is made of the possible ways in which complex wavefunctions might arise in molecular problems. Apart from situations of degeneracy, where they are optional, or in the presence of a magnetic field, where they are obligatory, they may in principle occur (i) in certain uses of the Born-Oppenheimer approximation, (ii) in certain variational calculations where restricted variation is made, (iii) in transforming certain types of real configuration-interaction wavefunctions into a simple orbital form, where the individual orbitals may turn out to be complex, and (iv) in perfect-pairing wavefunctions for molecules with abnormal valence angles. The conditions under which complex functions appear can sometimes be put in a general form, and examples are given. In cyclopropane, where the CCC valence angle is 60°, two distinct studies lead to the view that possibility (iv) seldom, if ever, occurs.

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