Group Function Theory of McWeeny

Perhaps the most systematic theoretical formulation of the problem of separable electron groups is due to McWeeny [65-67]. As mentioned above, the GF theory has served as the basis for various quantum chemical models and also for efficient treatments of the electron correlation problem in the framework of geminal methods [13, 79-81]. In the present context we emphasise rather the possible applications for the treatment of large molecules or aggregates. 

In the GF theory [65-67] the total AT-electron wave function is expressed in the form of a linear combination 

Of course, more general forms of the group functions are possible including fully correlated AT -electron wave functions which can always be expanded as linear combination of determinants. 

It is important to stress that only an approximate W wave function can be obtained if the partition of the electrons among different groups is kept fixed in all the configuration functions This approximation can be called the simplified group function (SGF) method [45], in contrast to the full method where all the possible partitions of the N electrons are allowed. Nevertheless the SGF approximation is quite good in all the cases where there are no important covalent interactions. This is the case for most of the van der Waals complexes and also for interacting two-electron bonds [81], or for fragments defined as an ensemble of localized bonds. 

In general one assumes that the group functions are strongly orthogonal, i.e. 

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