Title 



Exchange energy density and some approximate exchange potentials obtained from HartreeFock theory of the ground state of the Be atom


Author 





Abstract 



HartreeFock (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) exchangecorrelation potential exists for the Be atom, we have compared this with (a) the Slater potential VSL(r) = 2 epsilon (x)(r)/rho (r) and (b) the HarbolaSahni form. Both have the main features of the QMC exchangecorrelation potential, though the magnitude of VSL(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 LevyPerdew relation between the total exchange energy and the 'viriallike' form involving the gradient of the exchange potential. (C) 2001 Elsevier Science B.V. All rights reserved.  

Language 



English


Source (journal) 



Chemical physics letters.  Amsterdam 

Publication 



Amsterdam : 2001


ISSN 



00092614


Volume/pages 



343:12(2001), p. 166170


ISI 



000170144200025


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