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 Ce 3+ and U 5+ ions, group 16 monohydrides, group 17 monoxides, lanthanide hexachlorides ( [ C e C l 6 ] 3 −, [ P r C l 6 ] 3 −, and [ N d C l 6 ] 3 − ), actinyl ions ( [ U O 2 ] +, [ N p O 2 ] 2 + ), and tricarbonatoactinyl complexes ( [ U O 2 ( C O 3 ) 3 ] 5 −, [ N p O 2 ( C O 3 ) 3 ] 4 − ). We also compare the results to new spin–orbit-inclusive calculations by single-state and multistate multireference perturbation theory.