An Efficient and Accurate Formalism for the Treatment of Large Amplitude Intramolecular Motion

We propose a general approach to describe large amplitude motions (LAM) with multiple degrees of freedom (DOF) in molecules or reaction intermediates, which is useful for the computation of thermochemical or kinetic data. The kinetic part of the LAM Lagrangian is derived using a Z-matrix internal coordinate representation within a new numerical procedure. This derivation is exact for a classical system, and the uncertainties on the prediction of observable quantities largely arise from uncertainties on the LAM potential energy surface (PES) itself. In order to rigorously account for these uncertainties, we present an approach based on Bayesian theory to infer a parametrized physical model of the PES using ab initio calculations. This framework allows for quantification of uncertainties associated with a PES model as well as the forward propagation of these uncertainties to the quantity of interest. A selection and generalization of some treatments accounting for the coupling of the LAM with other internal or external DOF are also presented. Finally, we discuss and validate the approach with two applications: the calculation of the partition function of 1,3-butadiene and the calculation of the high-pressure reaction rate of the CH(3) + H → CH(4) recombination.