### Abstract

The method of reduced density matrices for obtaining the ground-state energy of an atomic system is developed, making full use of the symmetry relations for orbital and spin angular momentum. These, together with an extensive set of Hamiltonian-dependent identities, serve to decrease the number of parameters which must be varied in the density-matrix variational principle. With only a small number of parameters required, inequalities such as the Pauli restriction can then be enforced. Numerical calculations for C++ show the relative ineffectiveness of certain low-lying geminals (in the Γ(2) expansion) in reaching the Pauli restriction limit, and thus point the way to significant improvement.

Original language | English (US) |
---|---|

Pages (from-to) | 310-315 |

Number of pages | 6 |

Journal | Physical Review A |

Volume | 2 |

Issue number | 2 |

DOIs | |

State | Published - 1970 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*2*(2), 310-315. https://doi.org/10.1103/PhysRevA.2.310

**Some restrictions on the use of reduced density matrices in atomic calculations.** / Kijewski, L. J.; Percus, Jerome; Pratt, I. H.; Tranchina, J. P.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 2, no. 2, pp. 310-315. https://doi.org/10.1103/PhysRevA.2.310

}

TY - JOUR

T1 - Some restrictions on the use of reduced density matrices in atomic calculations

AU - Kijewski, L. J.

AU - Percus, Jerome

AU - Pratt, I. H.

AU - Tranchina, J. P.

PY - 1970

Y1 - 1970

N2 - The method of reduced density matrices for obtaining the ground-state energy of an atomic system is developed, making full use of the symmetry relations for orbital and spin angular momentum. These, together with an extensive set of Hamiltonian-dependent identities, serve to decrease the number of parameters which must be varied in the density-matrix variational principle. With only a small number of parameters required, inequalities such as the Pauli restriction can then be enforced. Numerical calculations for C++ show the relative ineffectiveness of certain low-lying geminals (in the Γ(2) expansion) in reaching the Pauli restriction limit, and thus point the way to significant improvement.

AB - The method of reduced density matrices for obtaining the ground-state energy of an atomic system is developed, making full use of the symmetry relations for orbital and spin angular momentum. These, together with an extensive set of Hamiltonian-dependent identities, serve to decrease the number of parameters which must be varied in the density-matrix variational principle. With only a small number of parameters required, inequalities such as the Pauli restriction can then be enforced. Numerical calculations for C++ show the relative ineffectiveness of certain low-lying geminals (in the Γ(2) expansion) in reaching the Pauli restriction limit, and thus point the way to significant improvement.

UR - http://www.scopus.com/inward/record.url?scp=18344373910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18344373910&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.2.310

DO - 10.1103/PhysRevA.2.310

M3 - Article

VL - 2

SP - 310

EP - 315

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 2

ER -