The optimal mixing coefficient C of the exchange energy E x and the electron-electron interaction part of the exchange-correlation energy W :
? in the formula for the total exchange-correlation energy E x , was expressed through the ratio of the kinetic T, and potential W, contributions to the correlation energy E,. This expression can be derived from a Heavyside step function model of the dependence of Wi, on the coupling parameter of the electron interaction A. Values of T, and W, obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of T,, W,, and C on the bond distance was demonstrated for the case of the H, molecule. T, and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate E x , is strongly dependent on the bond length and has to disappear for weak interaction/large bond distances. The potential of the exchange-correlation hole constructed for H, from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). 0 1996 John Wiley & Sons, Inc.
different quantities than the conventional ones used in ab initio quantum chemistry. They are defined with respect to the determinantal wave function of Koh-Sham orbitals rather than with respect to the Hartree-Fock determinantal wave function. We briefly recall the relevant definitions.