Effect of Frustrated Rotations on the Pre-Exponential Factor for Unimolecular Reactions on Surfaces: A Case Study of Alkoxy Dehydrogenation

If theory is to be able to predict the rates of catalytic reactions over extended ranges of temperature and pressure, it must provide accurate rate constants for elementary reaction steps, including both the activation energy and pre-exponential factor. A standing difficulty with this objective is the treatment of floppy modes in the partition function for the adsorbed species. This issue leads to limited accuracy in the pre-exponential factor computed for realistic systems. Here, we investigate the C-H bond breaking for a series of linear-chain alkoxides on Cu(110) using density functional theory because the results can be compared to the experimental data for the rate constants. The structural similarity of these species enables us to understand the systematic effect of the molecular size on the frustrated motions and pre-exponential factor. First, we discuss the complexities of finding the global minimum structure of the adsorbed species and highlight the high dimensionality of the configuration space to be sampled. Then, we analyze the motions of harmonic normal modes, including the motions of the underlying metal atoms, and compute the harmonic pre-exponential factors. To account for periodic frustrated rotations, we use the hindered rotor model: this motion significantly decreases the pre-exponential factor in the C-H bond breaking, the effect increasing with the molecular size. We also estimate the anharmonic effect using the Morse treatment of potentials. The activation energy and pre-exponential factor computed for CH3O are in excellent quantitative agreement with the experiment. The trends computed for the homologous series of alcohols are also reflected by the experiment.