Restricted Open-Shell Time-Dependent Density Functional Theory with Perturbative Spin-Orbit Coupling: Inclusion of Spin-Flip-Down States

Calculating electronically excited states for molecular systems with an electronic configuration that has two or more unpaired electrons remains a challenge in quantum chemistry. The electronically excited states are often hard to model due to the complex nature of the wave function. This especially holds in the case of heavy-element systems for which the treatment of spin-orbit coupling is crucial for a good description. To address this, we have modified the SOC-corrected restricted open-shell Kohn-Sham (ROKS) time-dependent density functional theory approach within the Tamm-Dancoff approximation (TDA). We have extended the ROKS-TDA-SOC method by including scalar relativistic spin-flip-down states (in addition to spin-conserved and spin-flip-up ones) from ROKS-TDA, which participate in the SOC state interaction. Our assessment shows that ROKS-TDA-SOC is able to efficiently calculate the lowest-lying SOC-split excitation energies in molecular systems that contain heavy elements and two or more unpaired electrons.