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Multireference self-consistent-field energies without the many-electron wave function through a variational low-rank two-electron reduced-density-matrix method

J. Chem. Phys. 127, 244105 (2007); doi:10.1063/1.2817602

Published 28 December 2007

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Gergely Gidofalvi and David A. Mazziotti
Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637, USA
The variational two-electron reduced-density-matrix (2-RDM) method allows for the computation of accurate ground-state energies and 2-RDMs of atoms and molecules without the explicit construction of an N-electron wave function. While previous work on variational 2-RDM theory has focused on calculating full configuration-interaction energies, this work presents the first application toward approximating multiconfiguration self-consistent-field (MCSCF) energies via low-rank restrictions on the 1- and 2-RDMs. The 2-RDM method with two- or three-particle N-representability conditions reduces the exponential active-space scaling of MCSCF methods to a polynomial scaling. Because the first-order algorithm [Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)] represents each form of the 1- and 2-RDMs by a matrix factorization, the RDMs are readily defined to have a low rank rather than a full rank by setting the matrix factors to be rectangular rather than square. Results for the potential energy surfaces of hydrogen fluoride, water, and the nitrogen molecule show that the low-rank 2-RDM method yields accurate approximations to the MCSCF energies. We also compute the energies along the symmetric stretch of a 20-atom hydrogen chain where traditional MCSCF calculations, requiring more than 17×109 determinants in the active space, could not be performed. ©2007 American Institute of Physics
History: Received 20 September 2007; accepted 1 November 2007; published 28 December 2007
Permalink: http://link.aip.org/link/?JCPSA6/127/244105/1
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KEYWORDS and PACS

Keywords
PACS
  • 31.50.Bc
    Potential energy surfaces for ground electronic states (atoms and molecules)
  • 31.15.Ne
    Self-consistent-field methods (atoms and molecules)
  • 31.15.Pf
    Variational techniques (atoms and molecules)
  • YEAR: 2007

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PUBLICATION DATA

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