Spin-dependent unitary group approach to the Pauli–Breit Hamiltonian. I. First order energy level shifts due to spin–orbit interactions

Abstract

In this paper, we investigate the application of the spin-dependent unitary group approach to many-electron systems in the Born–Oppenheimer and Pauli–Breit approximation. The unitary group approach form of the Pauli–Breit Hamiltonian is determined explicitly, which should enhance the usefulness of the spin-dependent formalism in applications. It is applied to determine the first-order energy level splitting due to spin–orbit and spin–other orbit interactions entirely in the unitary group framework. In particular, this work indicates the feasibility of a spin-dependent unitary group approach perturbation theory for the efficient calculation of spin-dependent operators. Our results are also discussed briefly in terms of the unitary group density matrix formalism. The energy level shifts due to spin–spin interaction will be investigated within the unitary group approach in the second paper of the series.