Schrödinger Theory from a “Newtonian” Perspective -- Quantal Density Functional Theory -- New Perspectives on Hohenberg–Kohn–Sham Density Functional Theory -- Nonuniqueness of the Effective Potential Energy and Wave Function in Quantal Density Functional Theory -- Approximations Within Quantal Density Functional Theory -- Analytical Asymptotic Structure in the Classically Forbidden Region of Atoms -- Analytical Asymptotic Structure At and Near the Nucleus of Atoms -- Application of the Q-DFT Hartree Uncorrelated Approximation to Atoms -- Application of the Q-DFT Pauli Correlated Approximation to Atoms and Negative Ions -- Quantal Density Functional Theory of the Density Amplitude: Application to Atoms -- Application of the Irrotational Component Approximation to Nonspherical Density Atoms -- Application of Q-DFT to Atoms in Excited States -- Application of the Multi-Component Q-DFT Pauli Approximation to the Anion–Positron Complex: Energies, Positron and Positronium Affinities -- Application of the Q-DFT Fully Correlated Approximation to the Helium Atom -- Application of the Q-DFT Fully Correlated Approximation to the Hydrogen Molecule -- Application of Q-DFT to the Metal–Vacuum Interface -- Many-Body and Pseudo Møller-Plesset Perturbation Theory within Quantal Density Functional Theory -- Epilogue.

This book is on approximation methods and applications of Quantal Density Functional Theory (QDFT), a new local effective-potential-energy theory of electronic structure. What distinguishes the theory from traditional density functional theory is that the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and the correlation contribution to the kinetic energy -- the Correlation-Kinetic effects -- are separately and explicitly defined. As such it is possible to study each property of interest as a function of the different electron correlations. Approximations methods based on the incorporation of different electron correlations, as well as a many-body perturbation theory within the context of QDFT, are developed. The applications are to the few-electron inhomogeneous electron gas systems in atoms and molecules, as well as to the many-electron inhomogeneity at metallic surfaces.