Chemical reactions lie at the heart of processes designed to meet our growing energy and material needs. The first step towards designing and optimizing chemical reactions involves identification of underlying mechanisms and quantification of rates. Quantum chemistry methods along with theories such as transition state theory (TST) are indispensable for this purpose and have played a pivotal role in elucidating mechanisms in recent decades.  While widely successful, conventional TST is relatively simplistic and can lead to inaccurate rates for many classes of reactions. Alternative, more accurate rate theories such as variational transition state theory (VTST) with multidimensional tunneling are well-established but incur exceptionally high computational costs which limits their widespread use. We aim to lower these costs to enhance reliability of rate predictions by adapting algorithms typically used in signal processing. I will present our algorithm – harmonic variety-based matrix completion (HVMC) - that leverages matrix completion methods, widely used to recover signals from noisy, incomplete data, to recover otherwise expensive second derivatives of energy for points on the minimum energy path of a reaction.  We demonstrate that the algorithm scales favorably with system size and establish a machine learning scheme that automates the identification of the subset of data that must be sampled for optimal, accurate recovery of eigenvalues of second derivatives constituting the reaction path for low-cost free energy calculations.

Beyond conventional transition state theory in catalysis: Applications of matrix completion algorithms

ACS Fall 2021

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