Noncollinear Spin-Flip TDDFT for Potential Energy Surface Crossings: Conical Intersections and Spin Crossings

We recently proposed a scheme to generalize collinear functionals to the noncollinear regime, termed the multicollinear approach, which preserves spin symmetry and provides numerically stable higher-order functional derivatives. This scheme has been applied to noncollinear spin-flip time-dependent density functional theory (TDDFT) and its analytic gradient calculations. In the present work, with the aid of the penalty function method, we employ the noncollinear spin-flip TDDFT in the multicollinear scheme to locate potential energy surface crossings. We investigate two distinct types of crossings and analyze their topographical and spin characteristics near the crossing points. The first type is conical intersections between states of the same spin multiplicity, such as the singlet ground and excited states. The second type involves spin crossings that occur between electronic states with different spin multiplicities, such as between singlet and triplet. These crossing regions enable ultrafast nonadiabatic transitions through either nonadiabatic coupling or spin-orbit coupling, playing a crucial role in photochemistry. Through theoretical analysis and illustrative examples, we demonstrate the advantages of noncollinear spin-flip TDDFT over conventional collinear spin-flip TDDFT or spin-conserving TDDFT. Finally, we systematically evaluate its prospects as an electronic structure method for use in nonadiabatic molecular dynamics.