On the development of non-adiabatic functionals in real-time TDDFT

Time-Dependent Density Functional Theory (TDDFT) has made remarkable achievements in the description of excitation spectra and response properties. On the other hand, for the description of dynamical processes in the non-linear regime, the adiabatic approximation is widely used, with groundstate DFT functionals that depend only on the instantaneous density. In systems driven far from equilibrium, memory-dependence can dramatically affect the shape of the exact exchange-correlation potential, and as a result, adiabatic approximations give poor predictions of the dynamics.
Starting from an exact expression of this potential we derive a simple non-adiabatic and non-local approximation. We study this approximation for several numerically exactly-solvable model systems, for a range of physical situations: field-free dynamics of superposition states, laser-driven dynamics, and scattering.