Exposition of the Semiempirical Method

In any event, whether we derive the modified formula for either the total or the interaction energy, we will need Slater s generalization of the valence-bond method. Before we proceed, however, it may be well to warn the reader that the approximations made in deriving and applying the modified London formula are legion and clearly dubious. It is therefore indeed surprising that even rough relative results are obtained. 

we present a particular basic molecular system which is used for approximate applications in chemical kinetics. The presumption is that many other real systems have some of the character present in this basic system, which we now elaborate. Suppose we have n valence electrons and v nuclei, where n = r, and one valence electron is on each nucleus. Valence electrons may be regarded as those which enter more specially into bonding and therefore into a chemical reaction. Further, all the electrons will be in equivalent states. This latter provision means, for example, that all the coefficients of the terms in Eq. (80) are equal except for sign, and that and differ from each other only in interchange of equivalent nuclei. It should be noted that if we apply the results derived below to complex systems, i.e., not hydrogen atoms, we have made the doubtful assumption that we may ignore nonvalence electrons. Moreover, the equivalence of the electronic states imphes that we may treat complex systems as if all the valence electrons were in some particular state such as the Is state. 

No quarrel can exist as to the usual separationf of the electronic function tpjj) into spin functions, of or and position functions 

A general valence-bond position function could be 

One might suppose that any linear combination of such permuted functions is suitable. Actually, because of the Pauli exclusion principle only combinations which are antisymmetric with respect to electron interchange are allowed. Slater has shown how to formalize these with the determinant below as the basis  

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