Mapping the many-electron generalised spin-exchange Hamiltonian to accurate post-HF calculations

After some remarks about the theoretical foundations of the many-electron Heisenberg-Dirac spin Hamiltonian, we have investigated the transferability of the two-body spin-exchange parameter of this model mapping accurate post-Hartree-Fock results obtained for H2, H3 and H4 systems with the analytical solutions of the corresponding spin Hamiltonian. Highly symmetric structures, described by only one independent spin-exchange parameter, and less symmetric cases, described by two or three spin-exchange parameters have been analyzed. The generalized many-body Heisenberg-Dirac Hamiltonian is found to be suited to reproduce the ab initio values for Hn clusters (n = 2, 3, 4) when internuclear distances are larger that 3 Å, i.e., beyond the bonding region. Concerning the transferability of the two-electron spin exchange parameter (JH2) in this internuclear distance region, particular attention should be paid to the characteristics of the systems analyzed and to their relationship with the parent molecule (here H2), as underlined by the results obtained for H4 square planar system and linear H3 system.