High-Level Coupled-Cluster Energetics by Monte Carlo Sampling and Moment Expansions

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Piotr Piecuch of Michigan State University is supported by an award from the Chemical Theory, Models and Computational Methods program in the Chemistry Division to develop a radically new approach to solving the many-particle Schrodinger equation. This method holds the key to explaining the motion of electrons in atoms and molecules. By understanding the details of this motion, Piecuch and his group can precisely determine the amounts of energy needed to break chemical bonds and transform reactants into products. The ability to do these calculations accurately will ultimately aid in the design of new materials, better catalysts, and more efficient energy sources. The new approach uses repeated random tests of many small energy contributions and retains those found to be most important. This approach reduces the computational costs of high-accuracy methods by orders of magnitude. Once fully developed, the methods will be shared with the community via open-source mechanisms. Findings resulting from the activities are being used in teaching courses and communicated through publications, seminars, and conference presentations. These ideas provide positive training experiences in the forefront of the physical sciences for members of the Piecuch group. This research addresses one of the key challenges in electronic structure theory, namely the development of practical and systematically improvable ab initio computational schemes aimed at an accurate description of molecular energetics. It is widely accepted that size extensive methods based on the coupled-cluster theory are excellent candidates for addressing this challenge. However, it has been notoriously difficult to incorporate higher-than two-body components of the cluster operator, needed to achieve a quantitative description, without running into prohibitive computational costs of higher-order coupled-cluster schemes. The proposed methodology solves the problem, allowing one to obtain accurate energetics equivalent to high-level coupled-cluster calculations, even when electronic quasi-degeneracies and higher-than pair excitations become significant, at a small fraction of the computational cost. It also preserves the black-box character of conventional single-reference computations, by fusing the deterministic formalism, abbreviated as CC(P;Q) with the stochastic configuration interaction and coupled-cluster Monte Carlo approaches. The formal and algorithmic advances and efficient computer implementations will be accompanied by calculations of molecular potential energy surfaces relevant to spectroscopy, chemical reaction mechanisms and dynamics, and catalysis. The work provides important training for graduate students and postdoctoral fellows and the programs being developed will be widely shared with the broader theoretical community.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.