The derivation of a symmetry-adapted generalized spin Hamiltonian

Abstract

The formulation of a generalized spin Hamiltonian using the decomposition of double tensor operators into products of single tensor operators is reexamined critically using their transformation properties under parity, time reversal, charge and Hermitian conjugation, as well as the imposition of symmetry constraints. These properties depend on their polar or axial vector classification. It is concluded that limitations in the parameterization of experimental EPR and ENDOR spectral data are associated with an excessively restrictive interpretation of the constraints imposed in the derivation of phenomenological and generalized spin Hamiltonians. It is shown that the correct imposition of these constraints using the double tensor formulation leads to a symmetry adapted generalized spin Hamiltonian which includes additional zero field splitting terms characteristic of the various crystallographic groups and described by odd rank tensor operators whose matrix elements are nonzero provided account is taken of configuration interactions. It is noted that the conclusions derived are applicable to all physical systems that can be described by Hamiltonians formulated in terms of tensor operators.