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The foundations and limits of S=12 and S=1 spin Hamiltonians for systems with two unpaired electrons in two well-defined orbitals per site are discussed by merging accurate ab initio calculations in binuclear systems with the effective Hamiltonian theory. It is shown that, beyond the usual J₈₉S₈S₉ terms, the effective spin Hamiltonian necessarily introduces four-body spin operators in the S=12 case and biquadratic terms in the S=1 formalism. The order of magnitude of these additional terms can be rationalized from a quasidegenerate perturbation theory expansion starting from a Hubbard-type Hamiltonian. This permits to discuss the physical mechanisms governing the reduction from the all electron Hamiltonian to the spin-only Hamiltonians and the conditions under which a further reduction from a spin Hamiltonian to the simplest Heisenberg--Dirac--Van Vleck form is possible. The overall discussion is illustrated by numerical calculations of the magnetic coupling between two Ni^2+ cations in the K₂NiF₄ perovskite and between triply bonded carbon atoms in poly-ynes.
Moreira et al. (Thu,) studied this question.