### Abstract

We use the differential virial theorem (DVT) directly to display the approximate spatial dependence of the exchange-correlation (XC) force in He and Be, applying an exact integral constraint on the XC force, recently established by March and Nagy. In He, an analytic ground-state density n (r), combined with the DVT plus the von Weizsäcker single-particle kinetic energy, suffices to determine an approximate XC force. For Be, the XC force is calculated for the semiempirical fine-tuned Hartree-Fock density, as proposed by Cordero. However, for the single-particle kinetic energy, following Dawson and March, a phase θ (r) must be obtained by solving numerically a nonlinear pendulumlike equation.

Original language | English |
---|---|

Article number | 014501 |

Journal | Physical Review A |

Volume | 79 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 5 2009 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*79*(1), [014501]. https://doi.org/10.1103/PhysRevA.79.014501

**Use of the differential virial theorem to estimate the spatial variation of the exchange-correlation force -∂ VXC (r) ∂r in the ground states of the spherical atoms He and Be.** / Bogár, F.; Bartha, Ferenc; March, Norman H.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 79, no. 1, 014501. https://doi.org/10.1103/PhysRevA.79.014501

}

TY - JOUR

T1 - Use of the differential virial theorem to estimate the spatial variation of the exchange-correlation force -∂ VXC (r) ∂r in the ground states of the spherical atoms He and Be

AU - Bogár, F.

AU - Bartha, Ferenc

AU - March, Norman H.

PY - 2009/1/5

Y1 - 2009/1/5

N2 - We use the differential virial theorem (DVT) directly to display the approximate spatial dependence of the exchange-correlation (XC) force in He and Be, applying an exact integral constraint on the XC force, recently established by March and Nagy. In He, an analytic ground-state density n (r), combined with the DVT plus the von Weizsäcker single-particle kinetic energy, suffices to determine an approximate XC force. For Be, the XC force is calculated for the semiempirical fine-tuned Hartree-Fock density, as proposed by Cordero. However, for the single-particle kinetic energy, following Dawson and March, a phase θ (r) must be obtained by solving numerically a nonlinear pendulumlike equation.

AB - We use the differential virial theorem (DVT) directly to display the approximate spatial dependence of the exchange-correlation (XC) force in He and Be, applying an exact integral constraint on the XC force, recently established by March and Nagy. In He, an analytic ground-state density n (r), combined with the DVT plus the von Weizsäcker single-particle kinetic energy, suffices to determine an approximate XC force. For Be, the XC force is calculated for the semiempirical fine-tuned Hartree-Fock density, as proposed by Cordero. However, for the single-particle kinetic energy, following Dawson and March, a phase θ (r) must be obtained by solving numerically a nonlinear pendulumlike equation.

UR - http://www.scopus.com/inward/record.url?scp=58849142189&partnerID=8YFLogxK

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U2 - 10.1103/PhysRevA.79.014501

DO - 10.1103/PhysRevA.79.014501

M3 - Article

AN - SCOPUS:58849142189

VL - 79

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 1

M1 - 014501

ER -