Is-time-dependent-density-functional-theory-formally-exact？.pdfVIP

Is time-dependent density functional theory formally exact? J. Schirmer Theoretische Chemie, Physikalisch-Chemisches Institut, Universit¨at Heidelberg, D-69120 Heidelberg, Germany A. Dreuw Institut f¨ur Physikalische und Theoretische Chemie, Universit¨at Frankfurt, Germany D-60439 Frankfurt (Dated: May 18, 2006) 1 Abstract The general expectation that, in principle, the time-dependent density functional theory (TDDFT) be an exact formulation of the time-evolution of an interacting N-electron system is critically reexamined. It is demonstrated that the previous TDDFT foundation, resting on four theorems by Runge and Gross (RG) [Phys. Rev. Lett. 52, 997(1984)], is invalid because undefined phase factors corrupt the RG action integral functionals. Our finding confirms much of a previous analysis by van Leeuwen [Int. J. Mod. Phys. B 15, 1969(2001)]. To analyze the RG theorems and other aspects of TDDFT, an utmost simplification of the KS concept has been introduced, in which the ground-state density is obtained from a single KS equation for one spatial (spin-less) particle. The time-dependent (td) form of this radical Kohn- Sham (rKS) scheme, which has the same validity status as the ordinary KS version, has proved to be a valuable tool for analysis. The rKS concept is used to clarify also the alternative non- variational formulation of td KS theory. We argue that it is just a formal theory, allowing one to reproduce, but not predict th