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This paper aims at presenting a general and compact matrix expression of the exact kinetic energy operator in polyspherical coordinates adapted to the study of semirigid molecules. The internal coordi...
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Variational calculations of fermion second-order reduced density matrices by semidefinite programming algorithm

J. Chem. Phys. 114, 8282 (2001); doi:10.1063/1.1360199

Issue Date: 15 May 2001

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Maho Nakata, Hiroshi Nakatsuji, and Masahiro Ehara
Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan

Mitsuhiro Fukuda
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8852, Japan

Kazuhide Nakata
Department of Applied Physics, The University of Tokyo, Tokyo 113-8656, Japan

Katsuki Fujisawa
Department of Architecture and Architectural Systems, Kyoto University, Kyoto 606-8501, Japan
The ground-state fermion second-order reduced density matrix (2-RDM) is determined variationally using itself as a basic variable. As necessary conditions of the N-representability, we used the positive semidefiniteness conditions, P, Q, and G conditions that are described in terms of the 2-RDM. The variational calculations are performed by using recently developed semidefinite programming algorithm (SDPA). The calculated energies of various closed- and open-shell atoms and molecules are excellent, overshooting only slightly the full-CI energies. There was no case where convergence was not achieved. The calculated properties also reproduce well the full-CI results. ©2001 American Institute of Physics.
History: Received 24 July 2000; accepted 9 February 2001
Permalink: http://link.aip.org/link/?JCPSA6/114/8282/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.15.Pf
    Electronic structure of atoms and molecules: theory Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations) Variational techniques
  • 31.25.-v
    Electronic structure of atoms and molecules: theory Electron correlation calculations for atoms and molecules
  • 02.10.Yn
    Mathematical methods in physics Logic, set theory, and algebra Matrix theory
  • YEAR: 2001

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0021-9606 (print)   1089-7690 (online)
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REFERENCES (25)
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