Response Theory and Calculations of Spin-Orbit Coupling Phenomena in Molecules

Abstract

We review response theory and calculations of molecular properties involving spin-orbit interactions. The spin-orbit coupling is evaluated for reference states described by single- or multi-configuration self-consistent field wave functions. The calculations of spin-orbit related properties rest on the formalism of linear and quadratic response functions for singlet and triplet perturbations when no permutational symmetry in the two-electron operators is assumed and from which various triplet as well as singlet response properties are derived. The spin-orbit coupling matrix elements between singlet and triplet states are evaluated as residues of (multi-configuration) linear response functions, and are therefore automatically determined between orthogonal and non-interacting states. Spin-forbidden radiative transition intensities and lifetimes are determined from the spin-orbit coupling induced dipole transitions between two electronic states of different multiplicity and are obtained as residues of quadratic response functions. The potential of the theory and its range of applications is illustrated by a selection of recent investigations covering different molecular phenomena. The applications include second-order energy contributions, intensity rearrangement in electron spectra, calculation of predissociative lifetimes of dicationic states, assignment of triplet bands in absorption spectra, intersystem crossings and reactivity, external heavy atom effects on S-T transitions, phosphorescence spectra and radiative lifetimes of triplet states. We give an outlook on spin-orbit interaction induced phenomena in extended systems and on applications to general spin catalysis phenomena.