Quantal Density Functional Theory

Abstract

Quantal density functional theory (Q–DFT) is a physical local effective potential theory of electronic structure of both ground and excited states. It constitutes the mapping from any state of an interacting system of N electrons in a time-dependent external field as described by Schrödinger theory to one of noninteracting fermions in the same external field and possessing the same quantum-mechanical properties of the basic variables. Time-independent Q–DFT constitutes a special case. The Q–DFT mapping can be to any arbitrary state of the model system. Q–DFT is based on the ‘Quantal Newtonian’ second and first laws of both the interacting and noninteracting systems. As such it is a description in terms of ‘classical’ fields derived from quantal sources as experienced by each model fermion. The internal field components are separately representative of electron correlations due to the Pauli Exclusion Principle, Coulomb repulsion, kinetic effects and the density. Thus, as opposed to Schrödinger theory, within Q–DFT, the separate contributions to the total energy and local potential due to the Pauli principle, Coulomb repulsion, and the correlation contribution to the kinetic energy—the Correlation-Kinetic effects—are explicitly defined in terms of fields representative of these correlations. The local potential incorporating all the many-body effects is the work done in the force of a conservative effective field which is the sum of these fields. The many-body components of the energy are expressed in integral virial form in terms of the individual fields representative of the different electron correlations. Various sum rules for the model system such as the Integral Virial Theorem, Ehrenfest’s Theorem, the Zero Force and the Torque Sum Rule are derived. Q–DFT is explicated by application to both a ground and excited state of a model system in the low electron-correlation regime, and to a ground state in the Wigner high-electron correlation regime. A new characterization of the Wigner regime based on the newly discovered significance of Correlation-Kinetic effects is proposed. The multiplicity of potentials as obtained via Q–DFT which can generate the same basic variables, and the significance of Correlation-Kinetic effects in such mappings, is discussed. The Q–DFT of degenerate states is described, as is the Q–DFT of Hartree and Hartree-Fock theories.