Performance of Tamm-Dancoff approximation on nonadiabatic couplings by time-dependent density functional theory

The Tamm-Dancoff approximation (TDA), widely used in physics to decouple excitations and de-excitations, is well known to be good for the calculation of excitation energies but not for oscillator strengths. In particular, the sum rule is violated in the latter case. The same concern arises within the TDA in the calculation of nonadiabatic couplings (NACs) by time-dependent density functional theory (TDDFT), due to the similarities in the TDDFT formulations of NACs and oscillator strengths [C. Hu, H. Hirai, and O. Sugino, J. Chem. Phys. 127, 064103 (2007)]. In this study, we present a systematic evaluation of the performance of TDDFT/TDA for the calculation of NACs. In the cases we considered, including a variety of systems possessing Jahn-Teller and Renner-Teller intersections, as well as an example with accidental conical intersections, it is found that the TDDFT/TDA performs better than the full TDDFT, contrary to the conjecture that the TDA might cause the NAC results to deteriorate and violate the sum rule. The surprisingly good performance of the TDA for NACs is probably because the TDA can partially compensate for the local-density-approximation error and give better excitation energies in the vicinity of intersections of potential energy surfaces. Our study also shows that it is important to use the TDA based on the rigorous full-TDDFT formulation of NACs, instead of using it based on an alternative approximate formulation.