Quantal density functional theory

This thesis is concerned with studies in time-independent (TI) Quantal density functional theory (Q-DFT), and of its extension by us to the time-dependent (TD) case. Q-DFT is a description of the s-system of noninteracting Fermions with electronic density equivalent to that of Schrödinger theory. The total energy and corresponding local effective potential are defined in terms of classical fields whose sources are quantal expectations of Hermitian operators taken with respect to the Schrödinger wavefunction. The fields are separately representative of electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and Correlation-Kinetic and Correlation-Current-Density effects, the last two resulting, respectively, from the difference in the kinetic energy and current density of the Schrödinger and s-system. We demonstrate TI Q-DFT by application to the ground-state of the exactly solvable Hooke's atom, thereby explaining the contributions of the various electron correlations to the transformation from Schrödinger theory to the s-system. To make Q-DFT applicable, we develop a many-body perturbation theory within its framework. In this theory there exists a separate perturbation series representative of Pauli-Coulomb correlations and Correlation-Kinetic effects. At lowest-order, representative of Pauli correlations, the upper bound on the total energy is rigorous. We next derive via Q-DFT the analytical structure of the local effective potential in the classically forbidden asymptotic region of atoms, thereby delineating the separate Pauli, Coulomb, and Correlation-Kinetic contributions to this structure. Next, we demonstrate analytically and by numerical example, that Pauli and Coulomb correlations do not contribute to the discontinuity in the effective potential as the electron number passes through an integer value, but that it is solely a consequence of Correlation-Kinetic effects. Finally, we extend TI Q-DFT to the TD case by deriving the TD Schrödinger and s-system differential virial theorems. By extending adiabatic coupling constant perturbation theory to TD systems, we explain the relationship between Q-DFT and TD Kohn-Sham DFT in terms of electron correlations. We also derive various sum rules and integral virial theorems for the TD s-system. We conclude with directions for future research.