There are two different methods for the formation of antisymmetric wave functions for an N-electron system. According to the more common approach, the various permutations of the N-electron function are arranged into a Slater determinant. In this case, the advantages of vector coupling procedures cannot be utilized. An alternate method consists of application of the coefficients of fractional parentage (cfp) originally introduced by Racah48 for the simple situation of N equivalent electrons in SO (3). The antisymmetric N-electron wave function is then generated as a sum of products of the antisymmetric (N — 1)-electron function times a function for the Nth electron. The coefficients of this expansion are the cfp (cf. Section 2.3). The method has been extended by Horie17 and others15,21 and may be readily generalized to the problem at hand, i.e., to an arbitrary configuration of inequivalent electron states in an arbitrary point group G.
KeywordsMatrix Element Symmetric Group Young Tableau Electron Wave Function Tensor Operator
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