Local spin II

Equations are discussed for computing, from ah initio wavefunctions, average values of quantities like S_A. S_B which appear in the Heisenberg model Hamiltonian of magnetism. These equations are based on projection operators onto local regions of space. They result in local spin operators S_A which obey the definition of angular momentum operators and commute with each other. These averages are evaluated for UHF and CI wavefunctions for a few examples of closed and open shell molecules. The calculations are compared with the assumptions made in the Noodleman method for evaluating the parameters in the Heisenberg Hamiltonian and with various definitions of bond order.