CAREER: Direct Determination of Two-electron Reduced Density Matrices for Many-electron Atoms and Molecules

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David Mazziotti of The University of Chicago is supported by the Theoretical and Computational Chemistry 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 radical reactions in combustion and atmospheric chemistry, chemical phenomena occurring at equilibrium and non-equilibrium molecular geometries, and various strong correlation phenomena. The research aims to calculate the 2-RDM directly via two approaches: 1) Solution of the contracted Schrodinger equation; 2) Variational minimization of the energy with a 2-RDM constrained by N-representability conditions. Recent advances by the PI and his group show that their method can recover 96-100% of the correlation energy. A first-order semidefinite programming algorithm increases the efficiency of the calculations in both floating-point operations and memory by many orders of magnitude. The PI is continuing and extending a new annual publication that encourages secondary 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. This work is having a broader impact on our ability to perform quantum computations for many-particle systems with useful accuracy but without a wave function, and in encouraging students to foster interests in the mathematical sciences.