The Constrained Search Approach, Mappings to External Potentials, and Virial-Like Theorems for Electron-Density and One-Matrix Energy-Functional Theories

Abstract

Quantitative predictions by means of electronic wavefunctions, within the framework of the Schroedinger equation, continues to be quite cumbersome for systems large enough to be of interest because the dimensions of wavefunctions grow spacially as three times the number or electrons. Density functional theory provides an attractive alternative to wavefunctional theory because the electron density possesses only three dimensions no matter how large the system. Similarly, the reduced spacial one-matrix possesses only six dimensions regardless the size of the system. Furthermore, a formal justification for density functional theory arises from the fact, which is by now well-known, that a ground-state electron density contains implicitly all the information embedded within its ground-state wave-function. Specifically, as proved by Hohenberg and Kohn, a ground-state electron density contains sufficient information to determine the more complicated ground-state wavefunctions.1