History of Semiempirical Methods

It was soon obvious that ab initio methods would be impractical for the study of large polyatomic systems. Attempts were made to use empirically determined data to approximate the complicated integrals used in ab initio theory. All of the difficult three- and four-center integrals were ignored, and the one- and two-center terms were approximated using a mixture of functions based on atomic spectra and on formal theory. Procedures of this type, which have both experimental and theoretical components, are called semiempirical methods. 

Semiempirical methods, which did yield heats of formation, did not fare very well, and, at that time, it is safe to say that semiempirical methods were not popular. This was largely a result of their easily demonstrated poor performance. Parameters in semiempirical methods were still based on atomic spectral data and on ab initio results. This approach, although justified at the time, was later to be replaced by parameters based on molecular data. 

To trace the evolution of semiempirical methods, it is illustrative to start with the earliest semiempirical self-consistent field methods. 

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Here we skim over the field of semiempirical VB theory of the Jt-systems of benzenoids. Primary focus is on a systematic derivational development of a hierarchical sequence of VB models. Different VB-based models are addressed in different sections (2, 3,5, 6) here, and the overall development is summarized in the diagram at the conclusion of Sect. 7. Section 4 serves as an interlude on quantum chemical computational methods, with emphasis on the VB basis and its relationship to chemical structure — this being crucial for the following sections. Along the way we indicate some of the history and general characteristics of the models. The unifying view which emerges not only incorporates many aspects of past work but reveals avenues for future research. 

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