Estimating Free Energy Barriers for Heterogeneous Catalytic Reactions with Machine Learning Potentials and Umbrella Integration

Predicting the rate constants of elementary reaction steps is key for the computational modelling of catalytic processes. Within transition state theory (TST), this requires an accurate estimation of the corresponding free energy barriers. While sophisticated methods for estimating free energy differences exist, these typically require extensive (biased) molecular dynamics simulations that are computationally prohibitive with the first-principles electronic structure methods that are typically used in catalysis research. In this contribution, we show that machine-learning (ML) interatomic potentials can be trained in an automated iterative workflow to perform such free energy calculations at a much reduced computational cost as compared to a direct density-functional theory (DFT) based evaluation. For the decomposition of CHO on Rh(111), we find that thermal effects are substantial and lead to a decrease in the free energy barrier, which can be vanishingly small depending on the DFT functional used. This is in stark contrast to previously reported estimates based on a harmonic TST approximation, which predicted an increase of the barrier at elevated temperatures. Since CHO is the educt of the putative rate limiting reaction step in syngas conversion on Rh(111) and essential for the selectivity towards $\mathrm{C}_\mathrm{2+}$ oxygenates, our results call into question the reported mechanism established by microkinetic models.