Anti-Hermitian part of the contracted Schroedinger equation for the direct calculation of two-electron reduced density matrices

Journal Article · Thu Feb 15 00:00:00 EST 2007 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.75.022505· OSTI ID:20982104

Mazziotti, David A ^[1]

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1. Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)

A recent advance in the theory of the contracted Schroedinger equation (CSE), in which only the anti-Hermitian part of the equation is solved, permits the direct determination of ground-state two-electron reduced density matrices (2-RDM's) that yield 95%-100% of the correlation energy of atoms and molecules [D. A. Mazziotti, Phys. Rev. Lett. 97, 143002 (2006)]. Here we discuss in detail the anti-Hermitian contracted Schroedinger equation (ACSE) and its comparison to the CSE with regard to cumulant reconstruction of RDM's, the role of Nakatsuji's theorem, and the structure of the wave function. The ACSE is also formulated in the Heisenberg representation and related to canonical diagonalization. The solution of the ACSE is illustrated with a variety of molecules including H{sub 2}O, CH{sub 2}, NH{sub 4}{sup +}, HF, and N{sub 2}, and potential energy and dipole-moment surfaces are computed for boron hydride in a polarized double-{zeta} basis set. The computed 2-RDM's very closely satisfy known N-representability conditions.

• OSTI ID: 20982104
• Journal Information: Physical Review. A, Vol. 75, Issue 2; Other Information: DOI: 10.1103/PhysRevA.75.022505; (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
ATOMS
BORON HYDRIDES
CATIONS
DENSITY MATRIX
DIPOLE MOMENTS
ELECTRON CORRELATION
ELECTRONS
GROUND STATES
HEISENBERG PICTURE
HERMITIAN MATRIX
HYDROFLUORIC ACID
MATHEMATICAL SOLUTIONS
MOLECULES
NITROGEN COMPOUNDS
ORGANIC COMPOUNDS
POTENTIAL ENERGY
SCHROEDINGER EQUATION
SURFACES
WATER
WAVE FUNCTIONS