Introduction

Abstract

The introductory chapter provides a brief description of Quantal density functional theory (Q–DFT), a physical local effective potential energy theory of the electronic structure of matter. The theory is based on a more recent perspective of the Schrödinger theory of electrons. This is a perspective of the individual electron in a sea of electrons in the presence of external fields. The corresponding equation of motion is described by the ‘Quantal Newtonian’ second law for each electron, the first law being a special case for the description of stationary state systems. Q–DFT is also based on a further understanding of the first Hohenberg-Kohn theorem of density functional theory, and the concept derived therefrom of the properties that constitute the basic variables of quantum mechanics. The Introduction is a description of the forthcoming chapters in the context of their relationship to Q–DFT and to each other: Schrödinger theory from the new perspective; Q–DFT, the corresponding ‘Quantal Newtonian’ laws, and its application to model and realistic systems; the rigorous generalization of the Hohenberg-Kohn theorems to the added presence of an external uniform magnetostatic field; the subsequent generalization of Q–DFT to such an external field; the Hohenberg-Kohn, Runge-Gross and Kohn-Sham density functional theories; the further insights into the fundamental theorems of density functional theory via density preserving unitary transformations and corollaries; the physical interpretation via Q–DFT of the energy and action functionals and corresponding functional derivatives of Kohn-Sham theory, and of other aspects of traditional density functional and other local effective potential theories.