A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

Abstract

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study (https://doi.org/10.1063/5.0018326), exploits the low-rank character of the polynomial expansion of potential energy to recover, using a small sample, vibrational frequencies (square roots of nuclear Hessian eigenvalues) constituting the reaction path. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four SN2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H- transfer, with the exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

Towards Efficient Direct Dynamics Studies of Chemical Reactions: A Novel Matrix Completion Algorithm

“…The ground truth matrices for all reactions have 24 columns, chosen such that the eigenvalue spectra and resulting observables vary smoothly along the MEP. 29 Along similar lines to our previous HVMC study, we calculate zero-point energies (ZPEs), vibrational free energies at high temperature (G vib , 1000K), and the position and value of adiabatic ground state potential barrier (V AG ) and free energy barrier ( G CV T ). Furthermore, tunneling can significantly accelerate reaction rates especially at low temperatures and when the reaction step involves displacement of a low-weight atom, such as hydrogen (reaction classes 2, 3, and 4 above).…”

“…The reactions chosen for benchmarking PVMC performance are largely identical to those employed in our prior HVMC studies. 26,29 The reactions span gas phase, enzymatic, and…”

“…10 However, neglecting curvature eliminates the necessity of eigenvector information which makes ZCT more appropriate for this work, which focuses exclusively on recovery of eigenvalues. Similar to previous work, 29 we adapt the procedure described in the Pilgrim software to calculate…”

“…For the remaining reactions in which all 3 stationary points are available, this corresponds to the need for at least K = 2 additional columns. We put forth two criteria that need to be satisfied for the PVMC-recovered matrix to be considered accurate, along similar lines to our prior HVMC studies: 26,29 1. The maximum absolute deviations in G vib (1000 K) and ZPE constituting the MEP must be less than 10 kJ/mol (2.39 kcal/mol).…”

“…26 We demonstrate that both quantum (zero-curvature tunneling at 300 K, zero-point energy) and variational (vibrational free energy) e↵ects are accurately predicted for a wide range of reaction types with very low sampling required for S N 2 reactions (4.5-20% of all elements), low to moderate sampling needs for hydrogen atom transfer reactions (10-35%), and sampling in excess of 50% for only the most complex reaction step with an Ir catalyst that involves simultaneous transfer of one hydride and two protons (60%). 29 Therefore MC methods o↵er promising means to accelerate rate coe cient calculations using variational theories. However, our HVMC approach has one critical shortcoming.…”