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 = integral rho(r) epsilon(xc)(r) dr and the exchange-correlation potential upsilon(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 epsilon(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. upsilon(xc)(r) is likewise decomposed, and special features (bond midpoint peak, various types of step behavior) are identified and related to electronic correlation.