Generalization of Heisenberg Hamiltonians to non half-filled bands : a magneto-angular effective Hamiltonian for boron clusters

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Abstract
An effective Hamiltonian has been proposed for the study of the neutral states of boron clusters, i.e. for a 1/6th filled band. This generalization of Heisenberg Hamiltonians rests upon the definition of a model space spanned by products of ground state 2P(s2p) atomic wave-functions. The resulting effective Hamiltonian involves, besides Heisenberg-type effective spin exchange terms, angular-momentum exchange operators and spin-and-angular-momentum exchange operators. The logic of this effective Hamiltonian has been derived through 3d order quasi-degenerate perturbation theory. In practice the effective interactions are obtained from accurate MO-CI large basis set calculations on B2 through the use of a spectral definition of Heff. The transferability has been tested on the linear B3 system, by comparing the Heff predictions with accurate MO-CI results. The transferability proves to be satisfactory for the lower part of the spectrum. The model will be used for the treatment of the magnetic character of (possibly high spin) Bn linear chains. The role of hybridization processes has been discussed and the possible extension of this approach, derived from Anderson's rationalization of Heisenberg Hamiltonians, has been outlined

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