Solution of the 1,3-contracted Schroedinger equation through positivity conditions on the two-particle reduced density matrix
- Department of Chemistry and the James Franck Institute, University of Chicago, Chicago, Illinois 60637 (United States)
Correlation energies and reduced density matrices (RDMs) of atoms and molecules are directly computed by solving the 1,3-contracted Schroedinger equation (1,3-CSE). The solution of the 1,3-CSE synthesizes two optimization strategies recently employed for the direct determination of the 2-RDM: (i) variational minimization of the energy with respect to a 2-RDM constrained by positivity conditions [D. A. Mazziotti, Phys. Rev. A 65, 062511 (2002)] and (ii) the contracted power method for solving the 2,4-CSE [D. A. Mazziotti, J. Chem. Phys. 116, 1239 (2002)]. While both the 3- and the 4-RDMs in the 2,4-CSE are reconstructed from the 2-RDM by cumulant expansions, similar techniques cannot be directly applied to the 1,3-CSE because constructing the 2-RDM from the 1-RDM with cumulant theory does not improve upon the mean-field approximation. We, however, establish a unique mapping from the 1-RDM to the 2-RDM by searching for the 2-RDM, constrained by contraction and N-representability conditions, which minimizes the energy. The 2-RDM constrained search is practically implemented through recent advances in positive semidefinite programming. With the variational reconstruction of the 2-RDM and a cumulant reconstruction of the 3-RDM, the 1,3-CSE may be solved via a contracted power method for the ground-state energy and RDMs. The initial RDMs, it is shown, need not be N representable for the contracted power method to converge; this allows us to choose the original RDMs from a variational calculation with approximate N-representability conditions on the 2-RDM. Application of the 1,3-CSE algorithm to atoms and molecules yields highly accurate correlation energies both near and far from equilibrium geometries.
- OSTI ID:
- 20632433
- Journal Information:
- Physical Review. A, Vol. 66, Issue 6; Other Information: DOI: 10.1103/PhysRevA.66.062503; (c) 2002 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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