Parametrization of the two-electron reduced density matrix for its direct calculation without the many-electron wave function: Generalizations and applications
- Department of Chemistry and The James Franck Institute, The University of Chicago, Chicago, Illinois 60637 (United States)
An improved parametrization of the two-electron reduced density matrix (2-RDM) [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)] was recently shown to yield energies and properties that are markedly better than those calculated by traditional ab initio methods of similar computational scaling. In this paper a family of such energy functionals, generalizing the ones obtained previously, is derived through the use of (i) p-particle contraction relations based on the contraction of the cumulant expansions of p-particle RDMs and (ii) Cauchy-Schwarz relations that arise from an important set of N-representability constraints known as the two-positivity conditions. The 2-RDMs are explicitly parameterized in terms of the first-order part of the cumulant 2-RDM and, for the inclusion of single excitations, a second-order part of the 1-RDM. In contrast to earlier formulations based on the coefficients from configuration interaction with single and double excitations (CISD), the cumulant-based parametric 2-RDM methods, from the properties of cumulants, are rigorously size extensive. We also show that writing the energy functionals in terms of correlated 1-RDMs and cumulant 2-RDMs reduces the computational cost of the parametric 2-RDM methods to that of CISD. Applications are made to ground-state energies of several molecules, equilibrium bond distances, and frequencies of HF, F{sub 2}, and CO, the relative energy of the cis and trans isomers of HO{sub 3}{sup -}, and the HCN-HNC isomerization reaction. For bond breaking in hydrogen fluoride the improved and more efficient parametric 2-RDM methods yield energies with similar accuracies at both equilibrium and nonequilibrium geometries in 6-31G** and polarized valence quadruple-{zeta} basis sets. Computed 2-RDMs very nearly satisfy well-known N-representability conditions.
- OSTI ID:
- 21437891
- Journal Information:
- Physical Review. A, Vol. 81, Issue 6; Other Information: DOI: 10.1103/PhysRevA.81.062515; (c) 2010 The American Physical Society; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
BOND LENGTHS
CARBON MONOXIDE
CONFIGURATION INTERACTION
DENSITY MATRIX
ELECTRONS
EXCITATION
FUNCTIONALS
HYDROCYANIC ACID
HYDROFLUORIC ACID
ISOMERIZATION
ISOMERS
MOLECULES
VALENCE
WAVE FUNCTIONS
CARBON COMPOUNDS
CARBON OXIDES
CHALCOGENIDES
CHEMICAL REACTIONS
DIMENSIONS
ELEMENTARY PARTICLES
ENERGY-LEVEL TRANSITIONS
FERMIONS
FLUORINE COMPOUNDS
FUNCTIONS
HALOGEN COMPOUNDS
HYDROGEN COMPOUNDS
INORGANIC ACIDS
INORGANIC COMPOUNDS
LENGTH
LEPTONS
MATRICES
OXIDES
OXYGEN COMPOUNDS