Linearized Pair-Density Functional Theory with Spin–Orbit Coupling

We include spin–orbit coupling (SOC) effects in linearized pair-density functional theory (L-PDFT), which is a multistate extension of multiconfiguration pair-density functional theory (MC-PDFT). Both 1-electron and 2-electron SOC integrals are computed using Breit-Pauli and Douglas–Kroll–Hess Hamiltonians in the atomic mean-field approximation. SO-L-PDFT removes the unphysical J-symmetry breaking observed in MC-PDFT. The accuracy of SO-L-PDFT is validated by calculations of zero-field splittings, fine-structure excitation energies, and low-energy excited-state spectra for a diverse group of atoms and molecules spanning the whole range of the periodic table, including atoms of groups 3, 11, and 13–17, the Ce³⁺ and U⁵⁺ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ([CeCl6]³⁻[jls-end-space/], [PrCl6]³⁻[jls-end-space/], and [NdCl6]³⁻[jls-end-space/]), actinyl ions ([UO2]⁺[jls-end-space/], [NpO2]²⁺[jls-end-space/]), and tricarbonatoactinyl complexes ([UO2(CO3)3]⁵⁻[jls-end-space/], [NpO2(CO3)3]⁴⁻[jls-end-space/]). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.