Non-orthogonal orbitals for localized electrons: II. Variational optimization based on an effective spin hamiltonian Original Research Article

The derivation of an effective spin hamiltonian is achieved for a single configuration Spin-Coupled Valence Bond wavefunction built upon weakly overlapping non-orthogonal orbitals. The effective Spin-Coupled Magnetic Hamiltonian (SCMH) serves for the variational optimization of both orbital and spin parts of the wavefunction for larger numbers of electrons than genuine quantum-chemical methods. Optimized magnetic coupling terms are thus obtained. The method is applied to localized electrons within the one-dimensional half-filled Hubbard model yielding magnetic coupling constants that are in good agreement with reference Spin-Coupled calculations on finite size clusters and perturbation theory in the localized regime.