Approaches for Non-Adiabatic Functional Approximations in TDDFT

Several examples of electron dynamics in the non-perturbative regime highlight the need to go beyond the adiabatic approximation to achieve even a qualitatively reasonable description. This includes charge-transfer dynamics out of the ground-state, resonantly-driven dynamics, and cases of pump-probe spectroscopy. We discuss different approaches to develop functionals that build in memory into new non-adiabatic exchange-correlation functionals. In one, we develop density-matrix coupled exchange-correlation approximations, starting from an exact expression for the time-dependent exchange-correlation functional. In another, a time-dependent extension of the adiabatic connection formula is developed to take advantage of coupling-constant integration.