Valence bond theory avoided

In this review, research in the field of van der Waals molecules accomplished by our group in the last few years was summarised. On the basis of the results obtained so far, it appears that the modification of the Roothaan equations to avoid basis set superposition error at the Hartree-Fock level of theory is a promising approach. The fundamental development of the SCF-MI strategy to deal with electron correlation treatments in the framework of the valence bond theory has been described. A compact multistructure and size... 

It is important to appreciate clearly the distinction between SC theory and the older or classical valence bond theory. In classical VB theory, the orbitals are taken to be predetermined, either as simple atomic orbitals or hybrids of atomic orbitals. These hybrids, moreover, are fixed, for example, either as sp, sp, or sp, etc., -type orbitals. In SC theory, in contrast, no such preconceptions are imposed. The orbitals are optimized as linear combinations of basis functions (usually approximate AOs) much as in MO-based approaches. However, in common with classical VB theory, the SC orbitals in general overlap with one another (except, of course, in the case of orbitals of different symmetry), or, since the SC orbitals are often localized, by virtue of the physical separation between them. Generally speaking no constraints, apart from normalization, are applied to the SC orbitals and as a result they may be as localized or as delocalized as the situation demands. Bearing in mind that the SC orbitals are always singly occupied, this last means that their shapes are determined by whatever produces the optimum balance between the greatest extent of avoidance of the electrons in different orbitals and quantum interference effects, which arise from the overlap between orbitals. In practice, we have found that this invariably means that the SC orbitals turn out to be localized and indeed often resemble atomic or hybrid atomic orbitals, or semi-localized, meaning that the SC orbitals spread over two or, at most, three centres. 

The general question is whether the avoided crossing diagram is an oversimplified model or does it faithfully account for the barrier problem Specifically (i) Can the adiabatic curve be reproduced rigorously and shown to follow the energetic behavior that has been postulated by the qualitative theory (ii) Do the / G, and B parameters follow the predicted trends or estimations (iii) Can a mixture of only two valence bond curves reproduce an accurate adiabatic potential surface ... 

If we regard each electronic formula as dynamic rather than static, there is little to be gained by emphasizing the concept of resonance hybrids. Furthermore, the detailed theory of resonance has come under heavy fire. It is claimed by A. Burawoy that .. . the interpretation of polyatomic structures does not require the hypothesis of resonance among several idealized valence-bond structures, a speculative application of the quantum-mechanical conception of resonance, which is in disagreement with numerous facts. In view of this controversy, we shall avoid detailed application of the theory of resonance. The theory of molecular orbitals, an alternative treatment, is too complex for the present discussion. 

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