Introduction

Abstract

Quantal density functional theory (Q-DFT) is a new local effective potential energy theory of electronic structure. The definition of a local potential energy theory is the following. Consider a system of N electrons in an arbitrary time-dependent external field F ^ext (rt) such that F ^ext (rt)-∇v(rt). This system of interacting particles and its evolution in time is described by the non-relativistic time-dependent Schrödinger equation. Q-DFT is the construction of a model system of noninteracting Fermions whose density p(rt) is the same as that of the interacting system described by Schrödinger theory. The equivalent non-conserved total energy E(t) of the interacting system is also thereby obtained. The model system of noninteracting Fermions is referred to as the S system. As these Fermions are noninteracting, the effective potential energy of each Fermion is the same,and can therefore be represented by a local or multiplicative potential energy operator v _s (rt). The operator v _s (rt) is the sum of the external potential energy operator v(rt), and an effective electron-interaction potential energy operator v _ee(rt) that accounts for all the quantum many-body correlations. The corresponding S system wave function is a single Slater determinant of the noninteracting Fermion orbitals. The construction of such a model system is what is meant by a local effective potential energy theory. Thus, Q-DFT is a theory that describes the physics of transformation from the interacting Schrödinger system to one of noninteracting Fermions with equivalent density.