Exact modified-Hartree–Fock scheme through perturbation expansion of density matrices
✍ Scribed by A. Holas
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 239 KB
- Volume
- 69
- Category
- Article
- ISSN
- 0020-7608
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✦ Synopsis
In the modified-Hartree᎐Fock MHF approach, as defined by Baroni
Ž
. Ž . and Tuncel 1983 BT , the external potential is supplemented by a specific correlation Ž . 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 w viewed as describing a model noninteracting N-electron system analog of the Ž .
x 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 w x Ž . with a factor ␣ in the range 0, 1 , similarly as it was done by Levy and Perdew 1985 to link with the KS noninteracting system. An appropriate ␣-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 Ž . 1y␣ fraction of the electron repulsion energy, leads to an effective one-body nonlocal potential in an ␣-dependent Hamiltonian, the construction of which guarantees the density to be independent of ␣. Its ground-state solution serves for calculating F. This solution can be determined by means of the perturbation theory, with the unperturbed Ž . ␣s0 Hamiltonian generating the MHF determinantal wave function, in analogy to the Ž . Gorling and Levy 1993 approach with the KS function as the unperturbed one. Terms of ẗhe 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 ␣-dependent density matrices.