Exact relations of the quasienergy functional and the exchange-correlation potential from the Floquet formulation of time-dependent density functional theory

Abstract

Time-independent density functional theory ~DFT! of many-electron systems, based on the fundamental works of Hohenberg and Kohn @1# and Kohn and Sham @2#, is now a well established and practical tool in various branches of chemistry and physics @3#. Being a formalism of many-body theory in terms of the electron density r(r), DFT has proved to be accurate and computationally much less expensive than the ab initio wave functional methods, and this accounts for its great success in time-independent electronic-structure calculations of the ground states of many-electron systems. To study more interesting dynamical processes, one needs a time-dependent DFT ~TDDFT !@ 4‐7#. Runge and Gross @7# have developed a time-dependent Kohn-Sham theory by considering the action to be stationary with respect to the density variations. Several groups have also considered timedependent current density functional theory ~TDCDFT! recently @8‐10#, where the action needs to be stationary with respect to variations in paramagnetic current density as well as the density itself. The central result of the modern TDDFT and TDCDFT is a set of time-dependent Kohn-Sham ~TDKS! equations which are structurally similar to the timedependent Hartree-Fock ~TDHF! equations but include in principle exactly all many-body effects through a timedependent exchange-correlation potential. Recently we presented the Floquet formulation of TDDFT @11# and TDCDFT @12# for atoms and molecules in intense periodic and quasiperiodic ~multicolor !@ 13# time-dependent fields, allowing the reduction of TDKS equations to equivalent time-independent Floquet matrix eigenvalue problems. In the Floquet formulation of TDDFT, the main role is played by the quasienergy functional ~compare with the action functional in the general time-dependent formulation @7#!: