Positive Semidefinite Programming for Many-body Quantum Mechanics with Applications to Physical and Chemical Systems

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David Mazziotti of the University of Chicago is supported by the Theoretical and Computational Chemistry Program to compute two-particle reduced density matrices using recent advances in many-body theory and first-order positive definite programming. With this new ability to treat medium- to large-sized molecules, this methodology will provide geometries, bond polarities, excited-state transitions, transition state structures, and potential energy surface topologies both accurately and efficiently. Applications include molecular dissociation, singlet-triplet splitting in carbene chemistry, and quantum phase transitions in high-temperature metal-oxide superconductors.This research will lead to new, accurate methods for predicting chemical properties, and some aspects of the programming may be applicable to global economic models. In addition, high school students will be encouraged in the mathematical sciences through a new annual journal of their own publications.