How van der Waals Approximation Methods Affect Activation Barriers of Cyclohexene Hydrogenation over a Pd Surface

Inclusion of van der Waals (vdW) interactions in density functional theory (DFT) calculations improves the accuracy of the calculations of molecular structures, solid structures, and molecular adsorption configuration and energy. However, it remains unclear how vdW approximations affect calculations of activation barriers of surface reactions, which is valuable for evaluating the reaction kinetics. In this work, we choose a prototype reaction-cyclohexene hydrogenation on a Pd surface-as an example to compare different approaches to include vdW interactions in the calculation of activation barriers of surface elementary steps. We find that the adsorption of cyclohexene and desorption of the product, cyclohexane, are very sensitive to the approaches used to incorporate vdW interactions, while the intrinsic barrier of hydrogenation only varies by about 10%. As a result, the apparent activation barrier also varies to a large extent (from -1.90 to 0.28 eV). The rate-determining transition state was found to be the first hydrogenation step, independent of the vdW approximation used. These calculations indicate that the comparison of intrinsic (true) activation barriers between experimentally measured activation barriers and calculated values is more straightforward, while the comparison for the apparent activation energy may be less reliable. Therefore, simultaneous measurement of intrinsic and apparent activation barriers could serve as a potential way to benchmark the most reliable vdW approximation for molecular adsorption and reaction.