A Quantum Chemical View of Density Functional Theory

TLDR

Traditional quantum chemistry approaches to electron correlation are contrasted with density functional theory, highlighting how DFT’s exchange‑correlation energy and potential relate to correlation through density matrices and conditional amplitudes, and how the Kohn‑Sham orbital model differs from Hartree‑Fock definitions of exchange and correlation. The study aims to decompose the exchange‑correlation energy density into kinetic and electron‑electron potential components and present a practical method for calculating them from accurate wave functions to enable systematic improvement. The authors propose a practical approach that decomposes εxc(r) into kinetic and potential parts and calculates each from accurate wave functions. The exchange‑correlation potential is similarly decomposed, revealing features such as a bond‑midpoint peak and step behavior that are linked to electronic correlation.

Abstract

A comparison is made between traditional quantum chemical approaches to the electron correlation problem and the one taken in density functional theory (DFT). Well-known concepts of DFT, such as the exchange−correlation energy Exc = ∫ρ(r) εxc(r) dr and the exchange−correlation potential vxc(r) are related to electron correlation as described in terms of density matrices and the conditional amplitude (Fermi and Coulomb holes). The Kohn−Sham one-electron or orbital model of DFT is contrasted with Hartree−Fock, and the definitions of exchange and correlation in DFT are compared with the traditional ones. The exchange−correlation energy density εxc(r) is decomposed into kinetic and electron−electron potential energy components, and a practical way of calculating these from accurate wave functions is discussed, which offers a route to systematic improvement. vxc(r) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation.