Incorporating chemical information in matrix completion for efficient prediction of multidimensional tunneling corrections

Abstract

Quantum mechanical tunneling effects cannot be neglected when studying the kinetics of chemical reactions involving light atoms at low temperatures. Rate theories such as variational transition state theory with multidimensional tunneling (VTST/MT) can be computationally intensive as they need nuclear Hessian information along the entire minimum energy path (MEP) of the reaction step. We report an improved selection strategy for a small number of points on the MEP that are necessary for a low-cost reconstruction of Hessian eigenvalues via the the Polynomial Variety-based Matrix Completion (PVMC) algorithm [Quiton et al., Journal of Chemical Theory and Computation, 2022, 18, 4327] We combine chemically informed sampling of points on the MEP that correspond to crossings between critical bond distances with a Euclidean distance-based approach that identifies points on the MEP that are most dissimilar from already sampled ones. We examine the performance of PVMC with the new sampling approach in predicting zero-curvature tunneling transmission coefficients, VTST/MT-based kinetic isotope effects (KIEs), and their trends for two possible CH activation mechanisms catalyzed by dioxo-dicopper complexes. PVMC reduces Hessian evaluations by over 58% while maintaining high predictive fidelity, offering a computationally efficient approach for quantum chemical rate predictions. While the approach is accurate for small KIEs (≤ 10), the prediction of very large tunneling transmission coefficients and consequently KIEs (between 10 and 60) depend very strongly on the underlying sampling strategy. PVMC also assumes an approximate polynomial structure for Hessian eigenvalues, which cannot always capture sharp changes in eigenspectra in the vicinity of the transition state. Going forward, we aim to (1) identify alternative structures to the quasi-polynomial approximation and (2) MEP characteristics in addition to bond crossings, to develop a universal sampling and matrix completion scheme for inexpensive VTST/MT calculations.