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 E xc = ∫ρ( r ) ε xc ( r ) d r and the exchange−correlation potential v xc ( 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 ε xc ( 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. v xc ( r ) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation.