Towards Practical Matrix Completion Methods for Transition State Theory

Variational transition state theory (VTST) overcomes several of the shortcomings of the potential energy-based transition state theory (TST) in describing chemical reaction mechanisms and rates. However, because of its sheer computational cost resulting from prohibitive quantum mechanical hessians and entropy estimations, VTST is yet to be widely accepted compared to conventional TST in computational kinetics studies. In this work, we aim to reduce such costs by demonstrating that matrix completion algorithms, which exploit some underlying matrix structure in order to find missing elements, can be used to recover the frequencies of modes orthogonal to the minimum energy path (MEP). To this end, we not only develop the Harmonic Variety-Based Matrix Completion (HVMC) algorithm but also use a machine learning approach to optimize the sampling of hessians along the MEP for maximum accuracy.

We demonstrate proof-of-concept of HVMC with the MEPs of several reactions. We find that HVMC recovers the missing frequencies to high fidelity even with most elements randomly missing and that sampling requirements decrease as system size increases. Furthermore, we show that column-based sampling methods still recover the frequencies with low error, and we can augment the algorithm to take advantage of apparent row-based polynomial structures for even greater performance. With this success, our future work will therefore focus on furthering the practicality of HVMC which includes utilizing gradient-based methods to compute initial approximate eigenvalues, computing cheap eigenmodes from molecular mechanics hessians, and augmenting HVMC to handle noisy data