Non-perturbative dynamics with TDDFT: How to make best use of the adiabatic approximation - and go beyond

Time-dependent density functional theory (TDDFT) continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics, but reliability of its predictions is hampered by the use of the adiabatic approximation. This is particularly problematic for applications involving non-perturbative dynamics (e.g. excited-state dynamics, laser-driven or photo-induced dynamics) where significant features of the exact time-dependent exchange-correlation functional are known to be missing from these approximations. We reformulate TDDFT in this regime to instead use quantities obtainable purely from linear and quadratic response: this means that the functional is evaluated on a density close to the ground-state, instead of directly on the dynamically evolving density. We show that the response reformulation enables the same observables to be obtained as would be in the real-time formulation, while the same adiabatic functional approximation performs far better and more reliably. Examples including Ehrenfest dynamics, Rabi oscillations, and charge-transfer dynamics will be used to demonstrate this.