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Title
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Exchange energy density and some approximate exchange potentials obtained from Hartree-Fock theory of the ground state of the Be atom
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Author
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Abstract
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| Hartree-Fock (HF) theory of the ground state of the Be atom is used to calculate first the exchange energy density e(x)(r) from the Dirac density matrix. Beyond r = 2a(0), with a(0) = h(2)/me(2), epsilon (x)(r) rapidly approaches the general asymptotic form -1/2e(2)rho (r)/r, with p(r) the HF electronic density. The nuclear cusp condition 1/epsilon (x)(r) partial derivative epsilon (x)/partial derivativer /(r -->0) = -2Z/a(0) with atomic number Z = 4, is also accurately satisfied by the present numerical data. Since a quantum Monte Carlo (QMC) exchange-correlation potential exists for the Be atom, we have compared this with (a) the Slater potential V-SL(r) = 2 epsilon (x)(r)/rho (r) and (b) the Harbola-Sahni form. Both have the main features of the QMC exchange-correlation potential, though the magnitude of V-SL(r) at r = 0 is too large by some 16%. We have also studied how well these two approximate HF exchange potentials fare when inserted into the Levy-Perdew relation between the total exchange energy and the 'virial-like' form involving the gradient of the exchange potential. (C) 2001 Elsevier Science B.V. All rights reserved. |
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Language
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English
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Source (journal)
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Chemical physics letters. - Amsterdam, 1967, currens
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Publication
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Amsterdam
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2001
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ISSN
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0009-2614
[print]
1873-4448
[online]
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Volume/pages
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343
:1-2
(2001)
, p. 166-170
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ISI
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000170144200025
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Full text (Publisher's DOI)
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Full text (publisher's version - intranet only)
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