Exact modified‐Hartree–Fock scheme through perturbation expansion of density matrices

Abstract

In the modified-Hartree–Fock (MHF) approach, as defined by Baroni and Tuncel (1983) (BT), the external potential is supplemented by a specific correlation potential, such that the density (determined with the HF method) of an N-electron system in this modified potential is the same as the ground-state density of the exact many-body solution for this system in the original potential. The MHF equations may be viewed as describing a model noninteracting N-electron system [analog of the Kohn–Sham (KS) system], moving in a one-body effective potential—the sum of three local terms: external, electrostatic, and BT correlation, and of the nonlocal HF exchange. The present study introduces an adiabatic link between the fully interacting system and this MHF noninteracting system by scaling the two-body electron–electron interaction with a factor α in the range [0, 1], similarly as it was done by Levy and Perdew (1985) to link with the KS noninteracting system. An appropriate α-dependent functional F of the density n is defined using Levy constrained-search formulation of the density-functional theory. Density matrices serve as an indispensable tool. A term in F, representing the (1−α) fraction of the electron repulsion energy, leads to an effective one-body nonlocal potential in an α-dependent Hamiltonian, the construction of which guarantees the density to be independent of α. Its ground-state solution serves for calculating F. This solution can be determined by means of the perturbation theory, with the unperturbed (α=0) Hamiltonian generating the MHF determinantal wave function, in analogy to the Görling and Levy (1993) approach with the KS function as the unperturbed one. Terms of the perturbation expansion for the BT correlation energy and potential can be calculated self-consistently in this way. Expressions for the BT correlation energy are obtained also in a form of integrals over the coupling parameter, involving α-dependent density matrices. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 69: 469–483, 1998