Exact and approximate exchange potentials investigated in terms of their matrix elements with the Kohn-Sham orbitals

Journal Article · Thu Sep 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.032504· OSTI ID:20718530

Holas, A; Cinal, M ^[1]

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1. Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw (Poland)

Three approximate exchange potentials of high accuracy v{sub x}{sup Y}(r), Y=A,B,C, for the density-functional theory applications are obtained by replacing the matrix elements of the exact potential between the Kohn-Sham (KS) orbitals with such elements of the Fock exchange operator (within the virtual-occupied subset only) in three representations found for any local potential. A common identity is the base of these representations. The potential v{sub x}{sup C} happens to be the same as that derived by Harbola and Sahni, and v{sub x}{sup A} as that derived by Gritsenko and Baerends, and Della Sala and Goerling. The potentials obtained can be expressed in terms of occupied KS orbitals only. At large r, their asymptotic form -1/r is the same as that of the exact potential. The high quality of these three approximations is demonstrated by direct comparison with the exact potential and using various consistency tests. A common root established for the three approximations could be helpful in finding new and better approximations via modification of identities employed in the present investigation.

• OSTI ID: 20718530
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ACCURACY
ALGEBRA
ASYMPTOTIC SOLUTIONS
COMPARATIVE EVALUATIONS
DENSITY FUNCTIONAL METHOD
MATRIX ELEMENTS
POTENTIALS