Extended Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory for Charge-Transfer State

We propose a novel extended mixed-reference spin-flip time-dependent density functional theory (EMRSF-TDDFT). This approach extends MRSF-TDDFT by incorporating electronic configurations present in linear-response TDDFT but absent in conventional MRSF-TDDFT. The formulation is based on the connection between linear-response and MRSF time-dependent Hartree-Fock theories and is extended to TDDFT. Benchmark calculations for representative molecular systems show that the newly introduced configurations capture a major contribution to orbital relaxation effects. This stabilizes both ground and excited states described in the triplet-reference orbital basis and improves agreement with reference theoretical best estimates. We expect that the new EMRSF-TDDFT model is applicable to photochemical processes involving charge transfer.