Density functional theory for stationary states or ensembles is a formulation of many-body theory in terms of the particle density. Time-dependent density functional theory as a complete formalism is of more recent origin, although a time-dependent version. This chapter describes the linear-response limit of time-dependent density functional theory along with applications to the photo-response of atoms, molecules and metallic surfaces. Beyond the regime of linear response, the description of atomic and nuclear collision processes appears to be a promising field of application where the time-dependent Kohn and Sham (KS) scheme could serve as an economical alternative to time-dependent configuration-interaction calculation. So far, only a simplified version of the time-dependent KS scheme has been implemented in this context. Another possible application beyond the regime of linear response is the calculation of atomic multiphoton ionization which, in the case of hydrogen, has recently been found 54i55 to exhibit chaotic behavior. A full-scale numerical solution of the time-dependent Schriidinger equation for a hydrogen atom placed in strong time-dependent electric fields has recently been reported. A time-dependent Hartree–Fock calculation has been achieved for the multiphoton ionization of helium. For heavier atoms an analogous solution of the time dependent Kohn-Sham equations offers itself as a promising application of time-dependent density functional theory. © 1990 Academic Press, Inc.
Gross, E. K. U., & Kohn, W. (1990). Time-dependent density-functional theory. Advances in Quantum Chemistry, 21(C), 255–291. https://doi.org/10.1016/S0065-3276(08)60600-0