Relativistic four-component static-exchange approximation for core-excitation processes in molecules

A generalization of the static-exchange approximation for core-electron spectroscopies to the relativistic four-component realm is presented. The initial state is a Kramers restricted Hartree-Fock state and the final state is formed as the configuration-interaction single excited state, based on the average of configurations for (n-1) electrons in n near-degenerate core orbitals for the reference ionic state. It is demonstrated that the static-exchange Hamiltonian can be made real by considering a set of time-reversal symmetric electron excitation operators. The static-exchange Hamiltonian is constructed at a cost that parallels a single Fock matrix construction in a quaternion framework that fully exploits time-reversal and spatial symmetries for the D₂ₕ point group and subgroups. The K- and L-edge absorption spectra of H₂S are used to illustrate the methodology. The calculations adopt the Dirac-Coulomb Hamiltonian, but the theory is open ended toward improvements in the electron-electron interaction operator. It is demonstrated that relativistic effects are substantial for the L-edge spectrum of sulfur, and substantial deviations from the statistical 2:1 spin-orbit splitting of the intensity distribution are found. The average ratio in the mixed region is 1.54 at the present level of theory.