# Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories

## Abstract

In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to themore »

- Authors:

- Department of Physics, Peking University, Beijing 100871 (China)
- (United States)

- Publication Date:

- OSTI Identifier:
- 20982314

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032517; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; COULOMB FIELD; COUPLING CONSTANTS; DENSITY FUNCTIONAL METHOD; ELECTRONIC STRUCTURE; ELECTRONS; INTERACTIONS; NUCLEI; PAULI PRINCIPLE; PERTURBATION THEORY; POTENTIALS; SCHROEDINGER EQUATION; SPHERICAL CONFIGURATION; SYMMETRY; WAVE FUNCTIONS

### Citation Formats

```
Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210.
```*Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032517.

```
Qian, Zhixin, Sahni, Viraht, & Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210.
```*Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories*. United States. doi:10.1103/PHYSREVA.75.032517.

```
Qian, Zhixin, Sahni, Viraht, and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210. Thu .
"Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories". United States.
doi:10.1103/PHYSREVA.75.032517.
```

```
@article{osti_20982314,
```

title = {Asymptotic near-nucleus structure of the electron-interaction potential in local effective potential theories},

author = {Qian, Zhixin and Sahni, Viraht and Department of Physics, Brooklyn College and the Graduate School, City University of New York, Brooklyn, New York 11210},

abstractNote = {In local effective potential theories of electronic structure, the electron correlations due to the Pauli exclusion principle, Coulomb repulsion, and correlation-kinetic effects, are all incorporated in the local electron-interaction potential v{sub ee}(r). In previous work, it has been shown that for spherically symmetric or sphericalized systems, the asymptotic near-nucleus expansion of this potential is v{sub ee}(r)=v{sub ee}(0)+{beta}r+O(r{sup 2}), with v{sub ee}(0) being finite. By assuming that the Schroedinger and local effective potential theory wave functions are analytic near the nucleus of atoms, we prove the following via quantal density functional theory (QDFT): (i) Correlations due to the Pauli principle and Coulomb correlations do not contribute to the linear structure; (ii) these Pauli and Coulomb correlations contribute quadratically; (iii) the linear structure is solely due to correlation-kinetic effects, the contributions of these effects being determined analytically. We also derive by application of adiabatic coupling constant perturbation theory via QDFT (iv) the asymptotic near-nucleus expansion of the Hohenberg-Kohn-Sham theory exchange v{sub x}(r) and correlation v{sub c}(r) potentials. These functions also approach the nucleus linearly with the linear term of v{sub x}(r) being solely due to the lowest-order correlation kinetic effects, and the linear term of v{sub c}(r) being due solely to the higher-order correlation kinetic contributions. The above conclusions are equally valid for systems of arbitrary symmetry, provided spherical averages of the properties are employed.},

doi = {10.1103/PHYSREVA.75.032517},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}