On the use of the Breit–Pauli approximation for evaluating line strengths for spin-forbidden transitions. II. The symbolic matrix element method

Abstract

A procedure for constructing HsoCI using the symbolic matrix element method has been developed. Here Hso is the spin-orbit portion of the Breit–Pauli interaction and CI satisfies (H0−E0I) CI=O, where H0 is the nonrelativistic electronic Born–Oppenheimer Hamiltonian. When this procedure is used in conjunction with a recently developed algorithm for the determination of the corresponding first order perturbed wave function WI =VI +CI, using (H0 −E0I) VI =HsoCI [J. Chem. Phys. 83, 1168 (1985)] line strengths for spin-forbidden radiative processes can be determined for the large configuration state function expansions tenable within the context of direct configuration interaction procedures. Thus for systems for which the Breit–Pauli approximation is valid this methodology will permit determination of lifetimes for spin-forbidden transitions with an accuracy previously available only for spin-allowed processes. The potential of this methodology is illustrated by considering the spin-forbidden radiative process b1Σ+ → X 3Σ− in NF.