Non-adiabatic approximations in time-dependent density functional theory: progress and prospects

Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the calculations is limited by the available approximations for the exchange-correlation functional. In particular, it is known that the exact exchange-correlation functional has memory-dependence, but in practise adiabatic approximations are used which ignore this. Here we review the development of non-adiabatic functional approximations, their impact on calculations, and challenges in developing practical and accurate memory-dependent functionals for general purposes.