Exchange energy density and some approximate exchange potentials obtained from Hartree-Fock theory of the ground state of the Be atomExchange energy density and some approximate exchange potentials obtained from Hartree-Fock theory of the ground state of the Be atom
Faculty of Sciences. Physics

Department of Physics

article

2001Amsterdam, 2001

Physics

Chemistry

Chemical physics letters. - Amsterdam

343(2001):1-2, p. 166-170

0009-2614

000170144200025

E

English (eng)

University of Antwerp

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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