The 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 D_{2h} point group and subgroups. The $K$- and $L$-edge absorption spectra of H2S are used to illustrate the novelties of the methodology. The calculations adopts the Dirac--Coulomb Hamiltonian, but the theory is open-ended towards improvements in the electron-electron interaction operator. It is demonstrated that relativistic effects are substantial for the $L$-edge spectrum of sulphur, 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.