The valence-bond theory of molecular structure II. Reformulation of the theory

Abstract

The construction of spin eigenfunctions and the evaluation of matrix elements between them are discussed generally in preparation for a development of the valence bond (VB) theory along the lines indicated in I. The customary approximation of considering explicitly only the electrons outside a 'closed shell' is shown to be defensible. The reformulation of the VB theory is now straightforward, but its final description of bonding is quite new. Atomic orbitals (AO's) are replaced, whenever they appear, by orthogonalized atomic orbitals ($\overline{\text{AO}}$'s); but when the assumptions of the conventional theory are rigorously validated in this way the 'covalent' structures (now '$\overline{\text{VB}}$' structures) are found, quite generally, to indicate only strong repulsion between the 'bonded' atoms, and formal descriptions of bonding and of bond orders, in terms of 'spin-pairing', become nonsensical. Bonding can be described only by admitting into the wave functions polar $\overline{\text{VB}}$ structures; a bond between two atoms demands the appearance (with considerable weight) of pairs of structures differing by a 'charge hop' between the atoms concerned. The conventional VB structures are found to be equivalent to certain groupings of $\overline{\text{VB}}$ structures (non-polar and polar) and do, indeed, predict bonds between spin-paired atoms and repulsion between the atoms of different pairs. It is then possible to make full use of chemical intuition, using a plausible combination of conventional structures as a starting approximation in the more rigorous theory. A numerical illustration is provided by a discussion of the Kekule structures of benzene. Some important characteristics of energy calculations in the $\overline{\text{VB}}$ theory are pointed out. Quantities of intra- and inter-atomic origin are well separated, and the method is apparently well suited to development along either ab initio or empirical lines.