Time-dependent electronic structure methods provide an efficient, accurate, and robust alternative to traditional time-independent methods for computing both linear and nonlinear optical properties. With this in mind, we have developed the real-time Tamm-Dancoff approximation (RT-TDA). This approach models electron dynamics by propagating the linear-response time-dependent density functional theory (LR-TDDFT) amplitudes within the Tamm-Dancoff approximation (TDA) and adiabatic approximation. Because the electronic structure is propagated in real-time in a many-electron basis, RT-TDA overcomes known limitations of adiabatic Kohn-Sham RT-TDDFT for describing dynamics in intense fields. Acceleration by graphics processing units (GPUs) enables simulations of larger molecules and on longer time scales. To demonstrate the utility of our approach, we present the calculations of the linear absorption spectrum of a large organic molecule (120 heavy atoms), Rabi oscillations, and nonlinear 2-photon absorption, in which we observe the AC Stark effect.
Knoll et al. (2026) studied this question.