We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S1/T2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.
Nicole Bellonzi, Ethan Alguire, Shervin Fatehi, Yihan Shao, and Joseph E. Subotnik , "TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings", J. Chem. Phys. 152, 044112 (2020) https://doi.org/10.1063/1.5126440
The Journal of Chemical Physics