New algorithm for nonorthogonalab initio valence-bond calculations

Abstract

A new algorithm for nonorthogonalab initio valence bond calculation has been deduced based on the left-coset decomposition of the symmetric groupSN. The strategy in the new approach is that, instead of performing the summation overN! permutations of groupSN, we sum the left cosets, and each coset corresponds to a “positive determinant” of orderN/2 for the evaluation of overlap, or a few positive determinants for Hamiltonian. Therefore, the computation turns into accumulating positive determinants. The expressions for evaluating both overlap and Hamiltonian matrix elements of VB functions are given in detail. Our practice shows that such a positive determinant method is quite attractive and it provides an excellent starting point for developing an even much more efficient algorithm of nonorthogonal VB calculation.