On the number of configurations in an<i>N</i>-electron system

Abstract

Starting from some previously derived results, general closed-form expressions are given for the total number of configurations or structures, the number of configurations of a particular multiplicity, and the total number of antisymmetrized product functions (AP's), in an N-electron system. The number of electrons may be even or odd, and the number of orbitals may assume any value larger than 1/2N - 1 or 1/2(N - 1) in the N = even and N = odd cases, respectively. Some special cases are mentioned in which the formulae become particularly simple. The results are derived in view of comparing molecular orbital and valence bond calculations on actual molecules when both methods are used in their many-configuration aspect.