Reduced Scaling Many-Body Electronic Structure Methods: Improved Accuracy and Precision

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Edward Valeev of Virginia Polytechnic Institute and State University is supported by an award from the Chemical Theory, Models and Computational Methods Program in the Chemistry Division to develop efficient and accurate methods for studying the electronic properties of large molecules, crystalline solids, and interfaces. It is possible to predict the properties of matter around us by applying the laws of quantum mechanics to describe the behavior of electrons in atoms, molecules, and solids. Unfortunately, exact computational and theoretical modeling of electron behavior in systems with more than a few atoms is beyond the ability of even the most powerful supercomputers currently available due to the steep increase of computational cost with the number of electrons. Valeev and co-workers are developing methods that reduce the computational cost of accurate calculations by many orders of magnitude and make predictive simulations possible for systems with thousands of atoms. Such advances are crucial for our ability to design molecules and materials for particular functions, such as creating new catalysts for converting solar light into fuel. The methods developed are being included in widely-used software packages that may enhance research capabilities for national and international researchers.This project focuses on the development of many-body electronic structure methods (such as the diagrammatic perturbation theory and coupled-cluster) with reduced scaling with respect to system size (by exploiting low-rank and sparse structure of the operators and states) and precision (by building in the correct analytic structure via explicit correlation). This development builds upon recent advances by Valeev and co-workers that demonstrated that complete basis set coupled-cluster with singles, doubles, and perturbative triples calculations could be performed on closed-shell molecules with more than a thousand atoms. This project extends the approach to the treatment of molecules with open-shell electronic states, to manifolds of electronic states, and to electronic states of crystalline solids. The efficiency of the rank compression is being improved by tailoring representations to the particular electronic structure model. Lastly, the project applies these ideas to the high-order coupled-cluster models to extend their applicability to systems with 30-50 atoms. In addition to making these codes available through a widely-used software package, the work being done provides excellent training for graduate students and postdoctoral fellows.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.