Necessary conditions for the N-representability of the second-order reduced density matrix: Upper bounds on the P and Q matrices

Journal Article · Thu Mar 15 00:00:00 EDT 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.032502· OSTI ID:20982299

Neck, Dimitri Van ^[1]; Ayers, Paul W ^[2]

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1. Center for Molecular Modeling, Ghent University, 9000 Gent (Belgium)
2. Department of Chemistry, McMaster University, Hamilton, Ontario, Canada L8S 4M1 (Canada)

Usually, variational calculations for the second-order reduced density matrix are performed subject to the constraint that the 'P' and 'Q' matrices are positive semidefinite, which only constrains the lowest eigenvalue of these matrices. We characterize the highest eigenvalue of these matrices and discuss how the associated constraint (which is related to the ground-state energy of the Hamiltonians H=-P and H=-Q) can be implemented in practical calculations. This necessary condition for N-representability should help ensure that the second-order reduced density matrix is not 'overcorrelated'.

• OSTI ID: 20982299
• Journal Information: Physical Review. A, Vol. 75, Issue 3; Other Information: DOI: 10.1103/PhysRevA.75.032502; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
DENSITY MATRIX
EIGENFUNCTIONS
EIGENVALUES
GROUND STATES
HAMILTONIANS
VARIATIONAL METHODS