CAREER: Research and training in advanced computational methods for quantum and statistical mechanics

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Ab initio simulations have become widely used scientific workhorses with applications in physics, chemistry, materials science, and many related fields, but the reach of simulations is limited by computational complexity. To go beyond current capabilities in realistic and predictive ab initio simulations, it is necessary to address the current bottlenecks. This project aims to greatly enlarge the scope of ab initio simulations and open up major new areas for electronic-structure-theory-based predictive methodologies that are not possible today. This research lies at the intersection of multiple disciplines. The project connects advanced state-of-the-art techniques in computational mathematics to challenging problems arising from chemistry and materials science. The integrated research program will bring together ideas and techniques, which will not only help advance the application areas, but also has the potential to open up new research areas in mathematics.The research goal of this project is to innovate and analyze efficient algorithms based on advanced computational mathematics for electronic structure theory and computational statistical mechanics, which will greatly advance the scope of ab initio simulations with applications in chemistry, materials science, and many related fields. More specifically, topics considered include: (1) reduced scaling methods for electronic structure theory, which will extend the system size of the simulation; (2) efficient sampling algorithms for metastable systems, which will bridge the temporal scales; and (3) algorithms that go beyond Born-Oppenheimer approximation, which will give a more accurate account of quantum effects in classical dynamics. The educational objectives of this proposal are to prepare and train students for interdisciplinary research and to disseminate knowledge from graduate and undergraduate students to high school students and the general public in the U.S. and abroad.