Jacob's Ladder for Time-Dependent Density-Functional Theory: Some Rungs on the Way to Photochemical Heaven

摘要

The time-dependent extension of density-functional theory (TDDFT) provides a rigorous formalism allowing the treatment of electronic excitations and excited states. However, just as in traditional (ground-state) density-functional theory (DFT), the quality of the results depends upon the approximation used for the unknown exchange-correlation (xc) functional. Perdew and Schmidt have described the various functionals developed for ground state DFT in terms of a Jacob's ladder, where the rungs correspond to successive levels of approximation of the xc-functional. Within the adiabatic approximation, these functionals can also be used in TDDFT. However, TDDFT places additional demands on the functional that are not typically satisfied by approximations developed for the ground-state. The simple time-dependent local approximation already gives remarkably good results for many excited states. However other excitations require more accurate treatment of the xc potential. Our work on this problem will be summarized in terms of a "Jacob's ladder" adopted to the special needs of applied TDDFT.