Local spin

Equations are proposed for computing from ab initio wave functions quantiti es like [S-A.S-B], which appear in the Heisenberg model Hamiltonian of magn etism. These equations are based on projection operators derived from Lowdi n orthogonalization. They result in local spin operators S-A which obey the definition of angular momentum operators and commute with each other. Thes e equations are evaluated for several typical closed and open shell molecul es. For closed shells in the single Slater determinant approximation, [S-A. S-B] is -3/8 of the bond-order and [S(A)2] is +3/8 of the total number of b onds to center A. For open shells there are additional contributions from t he unpaired electrons. In favorable cases, these additional terms have the value assumed as the whole answer in the usual applications of the Heisenbe rg Hamiltonian. (C) 2001 American Institute of Physics.