QUANTAL DENSITY FUNCTIONAL THEORY

摘要

Traditional time-dependent (TD) density functional theory (DFT) is based on two postulates: the Hohenberg-Kohn theorem that the Schroedinger wavefunction for a system of electrons in an external field is a unique functional of the electronic density ρ(rt) to within a TD phase, and on the stationary action principle. The density is thereby obtained via the Euler equation. The theorem is proved for the case when the potential energy v(rt) of an electron in an external field is Taylor expandable about some initial time. However, the explicit functional dependence of the wavefunction on the density is not defined. The fact that the wavefunction is a functional of the density is explicitly employed in the Kohn-Sham (KS) version of the theory. The basic idea of KS DFT is to transform the physical system as described by the Schroedinger equation to one of noninteracting Fermions with equivalent density. We refer to these model Fermions as the S system, S being a mnemonic for 'single Slater' determinant. The existence of such an S system, referred to as noninteracting v-representability, has recently been proved for Taylor-expandable external potential energies. In the TD KS description of the S system, all the many-body effects are incorporated in an electron-interaction action functional A_(ee)~(KS)[ρ]. The corresponding effective electron-interaction potential energy v_(ee) (rt) of the S system Fermions is defined as the functional derivative δA_(ee)~(KS)[ρ]/δρ(rt). How the different electron correlations present within the S system are incorporated in the action functional A_(ee)~(KS)[ρ] or its functional derivative is not described by the theory.