Perturbation Theory Treatment of Spin–Orbit Coupling II: A Coupled Perturbed Kohn–Sham Method

A noncanonical coupled perturbed Kohn–Sham density functional theory (KS-DFT)/Hartree-Fock (HF) treatment of spin–orbit coupling (SOC) is provided. We take the scalar-relativistic KS-DFT/HF solution, obtained with a relativistic effective core potential, as zeroth-order approximation. Explicit expressions are given for total energy through 4th order, which satisfy 2n + 1 rule. Second-order provided orbital energies and variables spin-current DFT. Test calculations carried out on halogen homonuclear diatomic hydride molecules, including 6p 7p elements, well open-shell negative ions. The computed properties second or third order match those from reference two-component self-consistent field densities. In only one case (At2–) did significant deviation occur remaining variables. Our perturbation approach provides an efficient way adding effect SOC to single-reference treatment, in particular because it does not require diagonalization spinor basis, leading saving factors number required floating-point operations that may exceed magnitude.