Introduction

Abstract

In a recent book [1] entitled Quantal Density Functional Theory, referred to from now on in abbreviated form as QDFT, I described a new theory of the electronic structure of matter. Quantal density functional theory (Q-DFT) is the description [1–8] of a quantum-mechanical system of electrons in terms of “classical” fields and their quantal sources within the framework of local effective potential energy theory. The theory is based on a similar description of Schrödinger theory in terms of quantal sources and fields [1, 9, 10]. This “classical” description of a quantummechanical system is based on the integral and differential virial theorems of quantum mechanics [1–5,11]. The formal ideas underlying both time-dependent and time-independent Q-DFT as explicated in QDFT are within the Born–Oppenheimer Approximation [12]. As with Schrödinger theory, time-independent Q-DFT is a special case of the time-dependent theory. Q-DFT additionally provides insights into other traditional local effective potential energy theories. Thus, an understanding of Slater theory [13], and a rigorous physical interpretation of the Optimized Potential Method [14, 15] and of Hohenberg–Kohn–Sham density functional theory [16,17] are also provided in QDFT. (For the rigorous physical interpretation of time-dependent Runge–Gross [18] density functional theory via Q-DFT, the reader is referred to the literature [4–6].) In QDFT, further understandings in terms of electron correlations of the Local Density Approximation of Hohenberg–Kohn–Sham density functional theory and of the discontinuity issue [19] within local effective potential energy theory are also described. Hence, QDFT is comprised of the theoretical foundations of the theory, the further elucidation of the theory by application to the ground and excited states of an exactly solvable interacting model system, its relationship to and physical interpretation of other local effective potential energy theories, and of many fundamental insights arrived at via Q-DFT of the local effective potential energy approach to electronic structure.