On the optimal mixing of the exchange energy and the electron-electron interaction part of the exchange-correlation energy

Abstract

The optimal mixing coefficient C of the exchange energy Ex and the electron-electron interaction part of the exchange-correlation energy W1xc in the formula for the total exchange-correlation energy Exc was expressed through the ratio of the kinetic Tc and potential Wc contributions to the correlation energy Ec. This expression can be derived from a Heavyside step function model of the dependence of Wλxc on the coupling parameter of the electron interaction λ. Values of Tc and Wc obtained from ab initio wave functions were used to estimate C for a number of atoms and molecules. A strong dependence of Tc, Wc, and C on the bond distance was demonstrated for the case of the H2 molecule. Tc and C approach zero in the bond-dissociation limit; so for an electron-pair bond, the admixing of exact exchange to obtain an accurate Exc 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 H2 from an ab initio second-order density matrix was compared with its generalized gradient approximation (GGA). © 1996 John Wiley & Sons, Inc.