New implementation of mixed-reference spin-flip time-dependent density functional theory and application to molecules with variable diradical character and conical intersections.

Mixed-reference spin-flip time-dependent density functional theory (MRSF-TDDFT) improves upon the original spin-flip TDDFT (SF-TDDFT) approach by expanding the configurational space of the response states via a mixed-reference reduced density matrix, specifically, an equal mixture of the density matrices from the MS = +1 and MS = -1 components of the lowest triplet state. MRSF-TDDFT improves the description of the spin-flip target states and the respective energy differences and eliminates the problem of spin-contamination that often spoils the description of higher-lying states in SF-TDDFT. This article presents the theoretical framework and details of a new implementation of MRSF-TDDFT in the Q-Chem software package. The implementation includes calculations of energies and properties, including transition dipole moments, oscillator strengths, spin-orbit couplings, and density-matrix based analyses of the MRSF states and transitions. The capabilities of the theory are illustrated by applications to diradicals, butadiene, and a reduced retinal model, the penta-2,4-dieniminium cation, used to evaluate the performance of electronic structure methods in describing conical intersections.