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

This paper describes the development and testing of a polynomial variety-based matrix completion (PVMC) algorithm towards reducing computational effort associated with reaction rate coefficient calculations using variational transition state theory with multidimensional tunneling (VTST-MT). The algorithm recovers eigenvalues of quantum mechanical Hessians constituting the minimum energy path (MEP) of a reaction using only a small sample of the information, by leveraging underlying properties of these eigenvalues. In addition to the low-rank property that constitutes the basis for most matrix completion (MC) algorithms, this work introduces a polynomial constraint in the objective function. This enables us to sample matrix columns unlike most conventional MC methods that can only sample elements, which makes PVMC readily compatible with quantum chemistry calculations as sampling a single column requires 1 Hessian calculation. For various types of reactions – SN2, hydrogen atom transfer, metal-ligand cooperative catalysis, and enzyme chemistry – we demonstrate that PVMC on average requires only 6-7 Hessian calculations to accurately predict both quantum and variational effects.