Generalized product functions group

Key words Generalized product function - Group function - Ab initio model potentials - Embedding -Spectator groups... 

Here A is the antisymmetrizer for all particles and any given factor for sub stem R, describes the state of a group of Nr electrons. This ansatz is a generalized product function [1] - anaJogous to a Slater determinant, but with each spin-orbital replaced by a many-electron function. 

This kind of approach in which one distinguishes electron pairs as physically or chemically distinct subsystems has been extended by McWeeny in his theory of generalized product functions.99 In this model, one now distinguishes between several groups of electrons and writes the spatial wave-function in the form of a product of group functions ... 

A generalized product function, as defined in the title paper, is an antisymmetrized product of the d)Aa(l, , - a) individually antisymmetric wave functions describing the groups A in their electronic state a ... 

The original formulation of de Bruijn s theorem was for a quite general problem of this type, with a broad definition of the "weight" of a mapping. We assume that R is the union of a finite number of pairwise disjoint sets R- (i = 1,. .., k and that // is a direct product of groups //j, where //j acts on / j. For each there is a weight function where n is the number of elements of D that are... 

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