TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

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. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. This article appeared in N. Bellonzi et al., J. Chem. Phys. 152, 044112 (2020) and may be found at https://doi.org/10.1063/1.5126440.