# Explicitly correlated extracule densities for two-electron atoms

## Abstract

The spherical average d(R) of the electronic extracule density E(R) is the probability density function of finding the center-of-mass radius {vert_bar}r{sub j} + r{sub k}{vert_bar}/2 of any two electrons j and k to be R. For a particular class of correlated wave functions which explicitly include r{sub 12} terms, a method is presented to obtain the extracule density d(R). The method is applied to the ground-state helium atom and its isoelectronic analogs described by highly accurate Kionshita wave functions; also near-exact extracule densities d(R), their moments {l_angle}R{sup n}{r_angle} with n = {minus}2 to +4, and electron-electron counterbalance densities d(0) are determined. Comparison of the correlated results with the corresponding Hartree-Fock values shows that the electron correlation shifts the extracule density d(R) from a small to a large R region. Different roles of the radial and angular correlation contributions are also clarified in the electron correlation.

- Authors:

- Muroran Inst. of Tech., Hokkaido (Japan). Dept. of Applied Chemistry

- Publication Date:

- OSTI Identifier:
- 687546

- Resource Type:
- Journal Article

- Journal Name:
- International Journal of Quantum Chemistry

- Additional Journal Information:
- Journal Volume: 74; Journal Issue: 5; Other Information: PBD: 15 Sep 1999

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 66 PHYSICS; ATOMS; ELECTRONIC STRUCTURE; WAVE FUNCTIONS; HELIUM; GROUND STATES; ISOELECTRONIC ATOMS; CORRELATIONS; ELECTRON PAIRS

### Citation Formats

```
Koga, Toshikatsu, and Matsuyama, Hisashi.
```*Explicitly correlated extracule densities for two-electron atoms*. United States: N. p., 1999.
Web. doi:10.1002/(SICI)1097-461X(1999)74:5<455::AID-QUA3>3.0.CO;2-O.

```
Koga, Toshikatsu, & Matsuyama, Hisashi.
```*Explicitly correlated extracule densities for two-electron atoms*. United States. doi:10.1002/(SICI)1097-461X(1999)74:5<455::AID-QUA3>3.0.CO;2-O.

```
Koga, Toshikatsu, and Matsuyama, Hisashi. Wed .
"Explicitly correlated extracule densities for two-electron atoms". United States. doi:10.1002/(SICI)1097-461X(1999)74:5<455::AID-QUA3>3.0.CO;2-O.
```

```
@article{osti_687546,
```

title = {Explicitly correlated extracule densities for two-electron atoms},

author = {Koga, Toshikatsu and Matsuyama, Hisashi},

abstractNote = {The spherical average d(R) of the electronic extracule density E(R) is the probability density function of finding the center-of-mass radius {vert_bar}r{sub j} + r{sub k}{vert_bar}/2 of any two electrons j and k to be R. For a particular class of correlated wave functions which explicitly include r{sub 12} terms, a method is presented to obtain the extracule density d(R). The method is applied to the ground-state helium atom and its isoelectronic analogs described by highly accurate Kionshita wave functions; also near-exact extracule densities d(R), their moments {l_angle}R{sup n}{r_angle} with n = {minus}2 to +4, and electron-electron counterbalance densities d(0) are determined. Comparison of the correlated results with the corresponding Hartree-Fock values shows that the electron correlation shifts the extracule density d(R) from a small to a large R region. Different roles of the radial and angular correlation contributions are also clarified in the electron correlation.},

doi = {10.1002/(SICI)1097-461X(1999)74:5<455::AID-QUA3>3.0.CO;2-O},

journal = {International Journal of Quantum Chemistry},

number = 5,

volume = 74,

place = {United States},

year = {1999},

month = {9}

}