NN-VRCTST: Neural Network Potentials Meet Variable Reaction Coordinate Transition State Theory for the Rate Constant Determination of Barrierless Reactions

The determination of rate constants for barrierless reactions poses severe problems from a theoretical perspective. The main challenges concern the proper description of the electronic structure of the reacting system, which may have multireference character, the anharmonicity of the relative motions of the fragments, and the proper definition of the reaction coordinate. The literature state of the art in the context of transition state theory is its variable reaction coordinate implementation (VRC-TST), which overcomes these difficulties in determining the number of transition state ro-vibrational states through a Monte Carlo sampling of the potential energy surface (PES) defined by the relative orientation of the two fragments. Although approaching the accuracy of experiments, VRC-TST requires tens of thousands of single-point energy (SPE) evaluations, thus being computationally demanding. The approach developed in this work, named NN-VRCTST, aims at fitting the PES with physics-inspired artificial neural network (ANN) models to be used as surrogate potentials in VRC-TST simulations. The ANN efficacy is evaluated in the computation of high-pressure limit rate constants for gas-phase barrierless reactions and validated over state-of-the-art VRC-TST simulations. It is shown that the NN-VRCTST tool reaches an accuracy within 20% with respect to VRC-TST simulations performed by using traditional approaches. While lowering the number of SPE needed by at least a factor of 4, the computational framework devised here allows one to decouple ANN training and VRC-TST calculations, enabling the optimization of the SPE evaluations as well as the quality inspection of the employed data points. We believe that the NN-VRCTST approach has the potential to evolve into a robust and computationally efficient framework for performing VRC-TST calculations for barrierless reactions.