DOI: 10.1063/1.445800. An approximate universal energy functional in density functional theory

An approximate universal energy functional in density functional theory

10.1063/1.445800

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Using Harriman’s orthonormal set, a closed expression for the reduced first order density operator γ1(1,2)=ρ(1)1/2ρ(2)1/2G(1,2) is obtained in the context of the independent particle approximation. It is shown that G(1,2) is given by G(1,2)=(1/n)exp{i[(n+1)/2]F(1,2)}[sin 1/2 nF(1,2)]/sin 1/2 F(1,2)], where F(1,2)=f(r2)−f(r1). Using this representation of γ1(1,2), an approximate universal functional of the energy which is given solely in terms of ρ is constructed. In particular, closed analytic expressions for the kinetic and exchange energies are explicitly derived. The simplifications brought about in these expressions by spherical symmetry are also discussed.

Bibliography

LudeÃ±a, E. V. (1983). An approximate universal energy functional in density functional theory. The Journal of Chemical Physics, 79(12), 6174â6181.

Authors 1

Eduardo V. Ludeña (first)

References 33 Referenced 48

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Dates

Type	When
Created	22 years, 6 months ago (Feb. 28, 2003, 12:03 p.m.)
Deposited	1 year, 6 months ago (Feb. 9, 2024, 8:44 p.m.)
Indexed	2 months ago (July 2, 2025, 1:11 p.m.)
Issued	41 years, 8 months ago (Dec. 15, 1983)
Published	41 years, 8 months ago (Dec. 15, 1983)
Published Print	41 years, 8 months ago (Dec. 15, 1983)

Funders 0

None

BibTeX

@article{Lude_a_1983, title={An approximate universal energy functional in density functional theory}, volume={79}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.445800}, DOI={10.1063/1.445800}, number={12}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Ludeña, Eduardo V.}, year={1983}, month=dec, pages={6174–6181} }

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  "abstract": "<jats:p>Using Harriman\u2019s orthonormal set, a closed expression for the reduced first order density operator \u03b31(1,2)=\u03c1(1)1/2\u03c1(2)1/2G(1,2) is obtained in the context of the independent particle approximation. It is shown that G(1,2) is given by G(1,2)=(1/n)exp{i[(n+1)/2]F(1,2)}[sin\u2009 1/2 nF(1,2)]/sin\u2009 1/2 F(1,2)], where F(1,2)=f(r2)\u2212f(r1). Using this representation of \u03b31(1,2), an approximate universal functional of the energy which is given solely in terms of \u03c1 is constructed. In particular, closed analytic expressions for the kinetic and exchange energies are explicitly derived. The simplifications brought about in these expressions by spherical symmetry are also discussed.</jats:p>",
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