Abstract
It is shown that only a small piece of the exact universal variational functional of the one matrix is actually unknown. The unknown piece, EC[γ], is identified and several rigorous properties of EC[γ] are derived. Based upon the derived properties, approximate forms of EC[γ] are displayed for the purpose of actual calculations, Existence theorems are then proved which allow the “single-shot” determination of exact correlation energies directly from Hartree-Fock and exchange-only densities. In fact, all ground-state and excited-state properties of the system are determined by these densities. The existence theorems do not generally apply, however, a, to finite basis sets. EC [γ] is then compared with \({\tilde E_c}\left[ \rho \right]\) which is the “single-shot” universal correlation energy functional of the Hartree- Fock density which is put forth as the correction to the Hartree-Fock energy.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
REFERENCES
Several properties of EC [γ] have already been announced without proof. See M. Levy and J. P. Perdew, Int. J. Quantum Chem. Symp. (1985), in press.
T. L. Gilbert, Phys. Rev. B 12, 2111 (1975).
P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
M. Berrondo and 0. Goscinski, Int. J. Quantum Chem. S9, 67 (1975).
R. A. Donnelly and R. G. Parr, J. Chem, Phys. 69, 4431 (1978). See also R. A. Donnelly, J. Chem. Phys. 71, 2874 (1979).
J. K. Percus, Int. J. Quantum Chem. J 3, 89 (1978).
M. Levy, Proc. Natl. Acad. Sci. USA 76, 6062 (1979).
M. Levy, Phys. Rev. A 26, 1200 (1982).
S. M. Valone, J. Chem. Phys. 73, 1344, 4653 (1980).
E. H. Lieb, “Density Functionals for Coulomb Systems”, in Physics as Natural Philosophy: Essays in Honor of Lazlo Tisza on His 75th Birthday, H. Feshbach and A. Shimony, eds. M. I. T. Press, Cambridge (1982); E. H. Lieb, Int. J. Quantum Chem. 24, 243 (1983).
G. Zumbach and K. Maschke, J. Chem. Phys. 82, 5604 (1985).
E. V. Ludena and A. Sierraalta, Phys. Rev. A 32, 19 (1985).
A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).
E. H. Lieb, Phys. Rev. Lett. 46, 457 (1981).
M. Levy and J. P. Perdew, Phys. Rev. A 32, 2010 (1985).
See also related work in M Levy, W. Yang, and R. G. Parr, J. Chem. Phys. 83, 2334 (1985).
M. Levy, technical report, University of North Carolina Chapel Hill, 1975 (unpublished).
M. Levy and R. G. Parr, J. Chem. Phys. 64, 2707 (1976).
J. Katriel and E. R. Davidson, Proc. Natl. Acad. Sci. USA 77, 4403 (1980).
M. Levy, J. P. Perdew, and V. Sahni, Phys. Rev. A 30, 2745 (1984).
P. O. Lowdin, Phys. Rev. 97, 1474 (1955).
P. W. Payne, J. Chem. Phys. 71, 490 (1979).
R. A. Harris and L. R. Pratt, J. Chem. Phys. 83, 4024 (1985).
J. P. Perdew, Phys. Rev. B 33, 8822 (1986).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 D. Reidel Publishing Company
About this paper
Cite this paper
Levy, M. (1987). Correlation Energy Functionals of One-Matrices and Hartree-Fock Densities. In: Erdahl, R., Smith, V.H. (eds) Density Matrices and Density Functionals. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3855-7_25
Download citation
DOI: https://doi.org/10.1007/978-94-009-3855-7_25
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-8214-3
Online ISBN: 978-94-009-3855-7
eBook Packages: Springer Book Archive