Quantal Density Functional Theory of the Density Amplitude: Application to Atoms

Abstract

The Q-DFT of Chap. 3 is a description of the mapping from the interacting electronic system as defined by the Schrödinger equation of (2.1)–(2.5) to one of a model system of noninteracting fermions – the S system – with equivalent density ρ(r). Thus, via Q-DFT, an interacting system in a ground or excited state can be mapped into a model S system whose density is the same. The state of the S system is arbitrary, in that it could be in a ground or excited state (see Chap. 5). For an interacting system of N electrons, if the mapping is to an S system with the same electronic configuration, the S system differential equation with the same self-consistently determined local effective potential energy function v _s(r) must be solved N times. The resulting self-consistently determined single-particle spinorbitals lead to the equivalent density. A significant observation of the application of this Q-DFT to atoms (see QDFT and Chaps. 5, 10, 13, and 15) is that if the mapping is to an S system with the same configuration as that of the interacting system, the Correlation-Kinetic energy contributions are a very small fraction of the interacting system kinetic energy, and hence, from the virial theorem of the total energy. Thus, Correlation-Kinetic effects play a relatively insignificant role in such calculations, the contributions to the various atomic properties as obtained from the S system equations arising principally from correlations due to the Pauli principle and Coulomb repulsion.