| Notes: | Advisor: David A. Mazziotti.
Thesis (Ph.D.)--The University of Chicago, Division of the Physical Sciences, Department of Chemistry, 2009.
Dissertation Abstracts International, Volume: 70-12, Section: B, page: 7587.
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| Summary: | The electronic energy for a many-electron system is a known functional of the two-electron reduced-density-matrix (2-RDM). Unconstrained minimization of the energy with respect to the elements of the 2-RDM, however, produces energies that are far below the exact, full configuration interaction solution. One must impose certain N-representability conditions on the 2-RDM that guarantee the 2-RDM corresponds to a realistic N-electron density matrix. Recently, these conditions have been incorporated into a parametrization of the 2-RDM in terms of a set of single and double excitation coefficients. This parametric approach to variational 2-RDM theory is size-extensive and automatically generates nearly N-representable 2-RDMs for the determination of all 1- and 2-electron properties. I herein derive the topo-logical factor that enforces N-representability within the context of a singlet closed-shell many-electron system. The parametric 2-RDM method is generalized for the equivalent treatment of open- and closed-shell many-electron systems and achieves accuracies that surpass those of traditional electronic structure methods, specifically coupled cluster with single and double excitations (CCSD). The method is applied to a variety of open- and closed-shell systems, the optimization of geometric parameters for stable and transition structures, and the evaluation of harmonic vibrational frequencies. A local correlation framework is developed in which the local nature of electron correlation is exploited in order to treat large molecular systems that are typically too computationally demanding for treatment with the usual ab initio methodologies. Lastly, we elucidate the connections between the parametric 2-RDM method and other theories, specifically the coupled electron pair approximation (CEPA).
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