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 [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four S N2 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 sole 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.