A Quantum Chemical View of Density Functional Theory

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.