On the general theoretical foundations of methods for optimum hybrids

Abstract

This paper is intended as an attempt to establish a badly needed common theoretical background for different criteria for optimum hybrids. First, it is shown that hybridisation can be defined within the CI scheme and is not a specific feature of either the VB or the MO schemes. Next, using the MO scheme as a reference model, a description of the way in which hybrids follow from the search for bond orbitals is given. After analysing various physical and mathematical conditions, the hybrids thus defined are shown to be maximum-overlap hybrids, so that optimum hybrids determined by the maximum-localisation condition and hybrids determined by the maximum total overlap criterion coincide up to a choice of weights which is free in either case. Secondary hybridisation associated with lone pairs and redundant AO bases is shown to fit within the same general scheme. Its relation with orbital occupation is also discussed. Finally, the physical meaning of the various conditions and parameters (maximisation of overlap, orthogonality of hybrids, limiting form of lone pair hybrids, etc.) is discussed.