Electrostatic interpretation of an electron density associated with the spherical exchange-correlation potential <tex>$V_{xc}(r)$</tex> in atoms : application to Be
Electrostatic interpretation of an electron density associated with the spherical exchange-correlation potential <tex>$V_{xc}(r)$</tex> in atoms : application to Be
Faculty of Sciences. Physics

article

2002
Lancaster, Pa
, 2002

Physics

Physical review : A : atomic, molecular and optical physics. - Lancaster, Pa, 1990 - 2015

65(2002)
:3 Part b
, p. 1-3

1094-1622

1050-2947

034501

E-only publicatie

English (eng)

University of Antwerp

By means of an electrostatic analogy, an electron density is proposed that is related to the exchange-correlation potential V (xc)(r) in atoms. More precisely, such an electron density is best characterized by the amount of electronic charge Q (xc)(r), say, enclosed within a sphere of radius r centered on the atomic nucleus. Then Q (xc)(r) is related to the radial derivative of V (xc)(r) by Q (xc)(r) = -r(2)partial derivativeV (xc)/partial derivativer. \Q (xc)(r)\ tends to unity as r-->infinity and becomes zero in the limit r-->0. However, it increases at first as one comes away from the point at infinity, having the form at large r \Q (xc)(r)>1+2alpha/r(3)+O(1/r(4)), where alpha is the dipole polarizability of the singly charged positive ion. This means that \Q (xc)(r)\ must have at least one maximum, its height Q (xc)(r(m)) and its position r(m) then being important parameters characterizing the shape of Q (xc)(r). The intersection(s) with the line \Q (xc)\ = 1 are also plainly of importance in this same context. The exact form of Q (xc)(r) involves both fully interacting one- and two-particle fermion density matrices, as well as the orbitals of the Slater-Kohn-Sham (SKS) reference system. However, the example of Be is worked out, where it is shown that, if the ground-state density rho(r) = rho(SKS)(r) is known from either x-ray or electron diffraction experiments or from quantal computer simulation studies, then Q (xc)(r) can be derived for this light atom.

https://repository.uantwerpen.be/docman/irua/1bcebf/6711.pdf

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