Eugene Kamarchik Mazziotti Group Office: CIS E108 Telephone: 773-702-5218 Email: ekam@uchicago.edu

Research

Building on recent advances in reduced-density-matrix (RDM) theory for electronic structure, the RDM method is applied to systems of interacting nuclei to further the study of nuclear vibrations and ground-state nuclear motion.

A. Eugene DePrince III, E. Kamarchik, and D. A. Mazziotti. J. Chem. Phys. (submitted) "Reformulation of the constrained optimization in the parametric two-electron reduced-density-matrix method as a single unconstrained optimization."

E. Kamarchik and D. A. Mazziotti. Phys. Rev. Lett. 99, 243002. "Global energy minima of molecular clusters computed in polynomial time with semidefinite programming."

E. Kamarchik and D. A. Mazziotti, Phys. Rev. A 75, 013203. "Variational reduced-density-matrix method for ground-state nuclear motion."

Semidefinite Programming

Because electrons are indistinguishable and interact via pairwise forces, all chemically relevant information can be described by considering only two electrons. Thus, from the two-electron distribution which minimizes the energy, we can obtain all the properties of chemical interest. Similarly, for nuclei we can either approximate the interaction using empirical two-body interactions or treat the nuclei together with electrons in an ab initio fashion. A simple minimization of the energy with respect to the two-particle distribution, however, yields an energy much below that of the true ground-state since not all distributions correspond to physically meaningful systems. In order to solve this problem, known as the N-representability problem, we must impose constraints on the minimization. Such constraints lead to a class of problem called semidefinite programming. To solve the resulting semidefinite problem we have devloped the RRSDP algorithm which utilizes an augmented Lagrangian approach and guarantees the semidefiniteness by an RR' factorization.

Configuration Interaction

For small systems it is possible to calculate the exact solution to the Schrödinger equation within a limited basis set using full configuration interaction (FCI). Since the exact solution within a given basis must not interact with single or double excitations, this calculation can be made less computationally demanding by iteratively diagonalizing the Hamiltonian within the space of single and double excitations, yielding the ICI method.

Stochastic Methods

Several stochastic approaches to the problem of interacting nuclei have been investigated. These include, but are not limited to, diffusion quantum Monte Carlo and stochastic semidefinite program solvers.

Curriculum Vitae

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