Coulomb Holes and Correlation Potentials in the Helium Atom

Authors

Marlina Slamet, Sacred Heart UniversityFollow
Viraht Sahni, CUNY Graduate School and University Center

Document Type

Peer-Reviewed Article

Publication Date

4-1995

Abstract

In this paper we investigate Coulomb correlation effects in the He atom by studying the structure of the static and dynamic Coulomb hole charge distributions as determined by the analytical 39-parameter correlated wave function of Kinoshita. The static Coulomb hole, which is defined in terms of the radial electron-electron distribution function, shows that as a result of Coulomb repulsion there is a reduction in probability of electron approach within a distance of one atomic unit and an increase in this probability for greater separations. The dynamic Coulomb hole defined directly in terms of the pair-correlation density describes the probability of finding one of the electrons given the position of the other. We thus demonstrate how the two electrons are correlated as a function of the nonuniform density of the atom. We also investigate the correlation potential W_c(r) of the work formalism, which is the work done to move an electron in the force field of the dynamic Coulomb hole charge. The structure of W_c(r) is similar to the exchange potential W_x(r) (which is the work done to move an electron in the force field of the Fermi hole), in that it is attractive, monotonic, and has zero slope at the nucleus. However, as a result of the structure of the Coulomb hole for asymptotic electron positions, and the fact that its total charge is zero, the potential W_c(r) vanishes rapidly in the classically forbidden region.

Thus, the asymptotic structure of the exchange-correlation potential W_xc(r) of the work formalism is that of W_x(r) which is (-1/r). We also detemine via the Kinoshita wave function the correlation potential μ_c(r) of Kohn-Sham theory, which differs from W_c(r) in that it also incorporates the effects of the correlation contribution to the kinetic energy. Consequently, it is less attractive than W_c(r), but also has zero slope at the nucleus. However, as is known, the potential μ_c(r) is nonmonotonic, since it goes positive within the atom, then becomes negative in the classically forbidden region, finally vanishing asymptotically as a negative function. Since the exchange potentials of the work formalism and Kohn-Sham theory are the same for this atom, and because W_c(r) is strictly representative of Coulomb correlations, we attribute the nonmonotonicity and positiveness of the Kohn-Sham potential μ_c(r) to the correlation kinetic energy. This conclusion is consistent with the result that the difference between the correlation energies determined within the work formalism from the dynamic Coulomb hole and Kohn-Sham theory is equal to the correlation contribution to the kinetic energy.

DOI

10.1103/PhysRevA.51.2815

PubMed ID

9911913

Recommended Citation

Slamet, M. & Sahni, V. (1995). Coulomb holes and correlation potentials in the helium atom. Physical Review A, 51(4), 2815-2825. doi: 10.1103/PhysRevA.51.2815