Simulating Electron Dynamics with GPU-Accelerated Real-Time Tamm-Dancoff Approximation

TL;DR

The paper addresses the challenge of efficiently simulating ultrafast electron dynamics in large molecular systems. It introduces Real-Time Tamm-Dancoff Approximation (RT-TDA), propagating LR-TDDFT amplitudes in real time within the TDA and adiabatic frameworks, and implements it on GPUs within TeraChem. Key contributions include validation against TI-TDA for absorption spectra, demonstration of two-photon absorption pathways and AC Stark effects, and accurate reproduction of Rabi oscillations without dynamical detuning. Benchmarks show scalable GPU performance, enabling longer timescales and larger systems, with potential integration into mixed quantum–classical nonadiabatic dynamics workflows. Overall, RT-TDA offers a robust, efficient route to modeling nonlinear and strong-field electron dynamics in complex systems.

Abstract

Time-dependent electronic structure methods provide an efficient, accurate, and robust alternative to traditional time dependent methods for computing both linear and non-linear optical properties. With this in mind, we have developed the real-time Tamm-Dancoff approximation (RT-TDA). This is an approach to model 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 graphic processing units (GPUs) enables simulations of larger molecules and on longer timescales. To demonstrate the utility of our approach, we present the calculations of the linear absorption spectrum of a large organic molecule (120 heavy atoms), of Rabi oscillations, and of nonlinear 2-photon absorption, in which we observe the AC Stark effect.

Figures (6)

• Figure 1: The structure of compound 1 (F-Coronene). Carbon, nitrogen, and hydrogen atoms are showin in gray, blue, and white, respectively.
• Figure 2: Simulated absorption spectrum of the F-Coronene molecule with RT-TDA (blue) compared to reference TI-TDA (red).
• Figure 3: The structure of compound 2. Carbon, nitrogen, and hydrogen atoms are show in in gray, blue, and white, respectively.
• Figure 4: Simulation of nonresonant 2-photon absorption of compound 2, with laser frequency tuned to roughly half the excitation energy of the S2 state (excitation energy = 4.480 eV). The FWHM of the laser pulse is 30 fs. The intensity of the laser pulses is 5e-11Wcm, and the frequency is tuned to either a) exactly half of the excitation energy (2.240 eV; 5.416e14Hz), or b) 0.080 eV higher in energy (2.320 eV; 5.610e14Hz). Populations are obtained by projecting the time-dependent wave function onto the states that are obtained from TI-TDA at the same level of theory (see eq. \ref{['eq:populations']}).
• Figure 5: Populations of the ground state and S3 state ($\pi \rightarrow \pi^*$ excitation character) as a function of time. Populations are obtained by projecting the time-dependent wave function onto the states that are obtained from TI-TDA at the same level of theory (see eq. \ref{['eq:populations']}).