Exchange and correlation near the nucleus in density functional theory

Abstract

The near nucleus behavior of the exchange-correlation potential $v_{xc}(\mathbf{r})$ in Hohenberg-Kohn-Sham density functional theory is investigated. It is shown that near the nucleus the linear term of $O(r)$ of the spherically averaged exchange-correlation potential ${\bar{v}}_{xc}(r)$ is nonzero, and that it arises purely from the difference between the kinetic energy density at the nucleus of the interacting system and the noninteracting Kohn-Sham system. An analytical expression for the linear term is derived. Similar results for the exchange $v_x(\mathbf{r})$ and correlation $v_c(\mathbf{r})$ potentials are also obtained separately. It is further pointed out that the linear term in $v_{xc}(\mathbf{r})$ arising mainly from $v_c(\mathbf{r})$ is rather small, and $v_{xc}(\mathbf{r})$ therefore has a nearly quadratic structure near the nucleus. Implications of the results for the construction of the Kohn-Sham system are discussed with examples.

10 pages

References in corpus (1)

• Integral Coalescence Conditions In $D\ge 2$ Dimension Space

Cited by in corpus (4)

• Kohn-Sham Kinetic Energy Density in the Nuclear and Asymptotic Regions: Deviations from the Von Weizsäcker Behavior and Applications to Density Functionals
• Energy Density Functionals From the Strong-Coupling Limit Applied to the Anions of the He Isoelectronic Series
• Exchange-Correlation Potentials and Energy Densities through Orbital Averaging and Aufbau Integration
• Bounds for the second and the third derivatives of the electron density at the nucleus