Derivative couplings between TDDFT excited states obtained by direct differentiation in the Tamm-Dancoff approximation

Working within the Tamm-Dancoff approximation, we calculate the derivative couplings between time-dependent density-functional theory excited states by assuming that the Kohn-Sham superposition of singly excited determinants represents a true electronic wavefunction. All Pulay terms are included in our derivative coupling expression. The reasonability of our approach can be established by noting that, for closely separated electronic states in the infinite basis limit, our final expression agrees exactly with the Chernyak-Mukamel expression (with transition densities from response theory). Finally, we also validate our approach empirically by analyzing the behavior of the derivative couplings around the [12pt]{minimal}{document}T₁{document}T1/[12pt]{minimal}{document}T₂{document}T2 conical intersection of benzaldehyde.