CDS&E: Two-electron Reduced Density Matrices in Quantum Chemistry and Physics

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David Mazziotti of the University of Chicago funded by an award from the Chemical Theory, Models and Computational Methods program for developing new approaches to quantum chemistry. Discovering novel molecules and materials that are optimal for capturing energy from the sun or fighting disease in the human body requires detailed knowledge of the distributions of their electrons. Electrons, however, are very small particles; in fact, they are 1000 times less massive than a single hydrogen atom. Consequently, electrons obey the laws of quantum mechanics. Like Schrödinger's famous cat, who is paradoxically both half alive and half dead simultaneously, electrons can be found in two or more physical states at the same time. When electrons in a molecule occupy many more states than the number of electrons, the electrons in the molecule are described by scientists as being strongly correlated (or entangled). Strongly correlated electrons are present in some of the most fascinating molecules and materials from the transition-metal catalysts in nitrogen fixation to the copper-oxide planes in high-temperature superconductors. Despite the importance of strongly correlated electrons, however, the computational cost of describing them by the laws of quantum mechanics traditionally increases exponentially with the number of electrons, dramatically limiting the number of strongly correlated systems describable by theoretical chemistry and physics. In this project, Mazziotti and his research group are further developing a novel approach to strongly correlated molecules in which the energies and properties are computed as functions of only two electrons in the "sea" of charge from the remaining electrons. These so-called two-electron reduced density matrix (2-RDM) methods are able to treat strongly correlated molecules efficiently and accurately with a computational cost that does not grow exponentially when the system becomes large. Recently, the 2-RDM method has been applied to several interesting and very different types of chemical systems, for example to model the efficient release of energy in firefly bioluminescence. Mazziotti and his research group are currently working to extend the 2-RDM methods to larger molecular systems as well as time-dependent phenomena with important implications for describing molecules in studies ranging from materials to medicine. Mazziotti also produces a journal for high school students named E = mc2 which publishes research by students. The journal provides a forum for encouraging high school students to pursue careers in the mathematical sciences. The many-electron wave function contains much more information than necessary to compute the important energies and properties of molecules and materials. Because electrons are indistinguishable with pairwise interactions, however, the wave function as the basic variable of quantum mechanics can be replaced by the two-electron reduced density matrix (2-RDM). With support from the NSF, Mazziotti and his research group are building upon their recent advances in 2-RDM methods with an emphasis on developing and improving 2-RDM methods for treating ground and excited states as well as time-dependent quantum systems. Several significant advances in the direct calculation of the 2-RDM for strongly correlated systems are being pursued including: (1) a low-scaling 2-RDM method, which can strongly correlate hundreds of orbitals, corresponding to wave functions that are intractable by conventional methods, and (2) a steady-state 2-RDM method that can determine the conductance of a molecule or material even in the presence of strong electron correlation. The research has important applications to modeling and predicting the electronic energies and properties including conductivity of a wide range of large strongly correlated molecular systems.