Two-electron Reduced Density Matrices in Quantum Chemistry and Physics

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David Mazziotti of The University of Chicago is supported by the Chemical Theory, Models and Computational Methods program for research to develop and implement quantum mechanical methods to compute the electronic structure of atoms and molecules. The goal of this work is the direct determination of the 2-electron reduced density matrix (2-RDM) without the wave function. Applications of this method include excited states and conical intersections in photo-excited chemical reactions in combustion and atmospheric chemistry, steady states in non-equilibrium molecular conductivity, energy transfer in materials and biological processes such as bioluminescence and light harvesting, and various strong correlation phenomena. The research aims to establish and improve 2-RDM methods for low-cost and strong- correlation computations via two general approaches: 1) Solution of the contracted Schrodinger equation; 2) Variational minimization of the energy with a 2-RDM constrained or parameterized by N-representability conditions. Recent advances by Dr. Mazziotti and his group show that their method can recover strong electron correlation in molecular systems like firefly luciferin as well as acene chains and sheets whose wave functions, if computable, would span an octillion or more molecular configurations or determinants. This work has a large impact on our ability to use quantum mechanics to study interesting, real-world systems that would be impossible with wave function methods. Dr. Mazziotti is continuing and extending a new annual publication that encourages high school students to pursue careers and research in the mathematical sciences. He is developing a graduate class that uses the general concept of reduced density matrices to unite areas of chemistry, physics and mathematics from electronic structure to quantum information.