Non-Perturbative Electron Dynamics: Making TDDFT as Reliable as it is in the Response Regime

Time-dependent density functional theory (TDDFT) is ubiquitous in calculations of electronic spectra and dynamics but, with the commonly-used adiabatic approximation, is not always reliable. Going beyond the adiabatic approximation has proven challenging, especially in the non-perturbative regime, while there has been some progress in the response regime for particular cases where non-adiabaticity is important (e.g. double-excitations, relaxation/viscosity). Here, we show that an in-principle exact reformulation of TDDFT exists, requiring exchange-correlation functionals only from ground-state, linear, and quadratic response regimes, in which fully non-perturbative electron dynamics can be captured. Because the functional is evaluated in a domain closer to the one in which adiabatic approximations are derived, the results in this response-reformulated TDDFT (RR-TDDFT) are far more accurate than those obtained from time-dependent Kohn-Sham equations using the same functional approximation. We show that phenomena like Rabi oscillations and dipole-switching, long thought to be out of reach for TDDFT, can be accurately captured in RR-TDDFT, and that it resolves unphysical instabilities that had previously been a puzzle to interpret. Further, RR-TDDFT enables exchange-correlation functional developments in the response regime beyond the adiabatic approximation, which have so far been more successful than those in the non-linear regime, to be exploited for non-perturbative dynamics, thus significantly broadening their range of applications, and we show that dressed TDDFT for double-excitations can now be used to describe fully non-perturbative dynamics that access states of double-excitation character.