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Journal of Chemical Physics / Volume 120 / Issue 5 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 120, 2095 (2004); http://dx.doi.org/10.1063/1.1636721 (10 pages)

The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions

Zhengji Zhao1, Bastiaan J. Braams2, Mituhiro Fukuda2, Michael L. Overton3, and Jerome K. Percus4

1Department of Physics, New York University, New York, New York 10003
2Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
3Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012
4Department of Physics and Department of Mathematics, Courant Institute of Mathematical Sciences, New York University, New York, New York 10012

(Received 16 October 2003; accepted 5 November 2003)

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions. The additional conditions (called T1 and T2 here) are implicit in the work of Erdahl [Int. J. Quantum Chem. 13, 697 (1978)] and extend the well-known three-index diagonal conditions also known as the Weinhold–Wilson inequalities. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Formulating the reduced density matrix computation using the standard dual formulation of semidefinite programming, as opposed to the primal one, results in substantial computational savings and makes it possible to study larger systems than was done previously. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree–Fock, singly and doubly substituted configuration interaction, Brueckner doubles (with triples), coupled cluster singles and doubles with perturbational treatment of triples, and full configuration interaction calculations. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q, and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations. © 2004 American Institute of Physics.

© 2004 American Institute of Physics

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KEYWORDS and PACS

Keywords

electronic structure, variational techniques, optimisation, ground states, energy states

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1636721

PUBLICATION DATA

ISSN

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

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    J. E. Mayer, Phys. Rev. 100, 1579 (1955).

    A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).

    C. Garrod and J. K. Percus, J. Math. Phys. 5, 1756 (1964)JMAPAQ000005000012001756000001.

    W. B. McRae and E. R. Davidson, J. Math. Phys. 13, 1527 (1972)JMAPAQ000013000010001527000001.

    M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, J. Chem. Phys. 114, 8282 (2001)JCPSA6000114000019008282000001.

    F. Weinhold and E. Bright Wilson, Jr., J. Chem. Phys. 47, 2298 (1967)JCPSA6000047000007002298000001.

    M. Nakata, M. Ehara, and H. Nakatsuji, J. Chem. Phys. 116, 5432 (2002)JCPSA6000116000013005432000001.

    A. E. Carlsson, Phys. Rev. B 56, 12058 (1997).

    A. Klein and R. M. Dreizler, Phys. Rev. A 57, 2485 (1998).

    J. Cioslowski and R. Lopez-Boada, J. Chem. Phys. 109, 4156 (1998)JCPSA6000109000011004156000001.

    H. Nakatsuji, Phys. Rev. A 14, 41 (1976).

    K. Yasuda and H. Nakatsuji, Phys. Rev. A 56, 2648 (1997).

    C. Valdemoro, Phys. Rev. A 45, 4462 (1992).

    D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002).

    D. A. Mazziotti, Phys. Rev. A 66, 062503 (2002).

    L. J. Kijewski and J. K. Percus, Phys. Rev. A 2, 1659 (1970).

    L. J. Kijewski, Phys. Rev. A 9, 2263 (1974).


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