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Title
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Slater's nonlocal exchange potential and beyond
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Author
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Abstract
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| The local density approximation (LDA) to the exchange potential V-x(r), namely the rho(1/3) electron gas form, was already transcended in Slater's 1951 paper. Here, using Dirac's 1930 form for the exchange energy density epsilon(x)(r), the Slater (SI) nonlocal exchange potential V-x(sl)(r) is defined by 2epsilon(x)(r)/rho(r). In spherical atomic ions, say the Be or Ne-like series, this form already has the correct behavior in both r --> 0 and r --> infinity limits when known properties of the exchange energy density E,(r) and the ground-state electron density rho(r) are invoked. As examples, some emphasis will first be given to the use of the so-called 1/Z expansion in such spherical atomic ions, for which analytic results can be obtained for both epsilon(x)(r) and rho(r) as the atomic number Z becomes large. The usefulness of the 1/Z expansion is directly demonstrated for the U atomic ion with 18 electrons by comparison with the optimized effective potential prediction. A rather general integral equation for the exchange potential is then proposed. Finally, without appeal to large Z, two-level systems are considered, with specific reference to the Be atom and to the LiH molecule. In all cases treated, the Slater potential V-x(sl)(r) is a valuable starting point, even though it needs appreciable quantitative corrections reflecting directly atomic shell structure. (C) 2004 Wiley Periodicals, Inc. Int J Quantum Chem 102: 64-71, 2005. |
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Language
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English
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Source (journal)
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International journal of quantum chemistry. - New York, N.Y., 1967, currens
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Publication
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New York, N.Y.
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Wiley
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2005
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ISSN
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0020-7608
[print]
1097-461X
[online]
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DOI
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10.1002/QUA.20352
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Volume/pages
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102
:1
(2005)
, p. 64-71
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ISI
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000227015600007
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Full text (Publisher's DOI)
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Full text (open access)
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