Neural Network Sampling of the Free Energy Landscape for Nitrogen Dissociation on Ruthenium

Reaction rates in heterogeneous catalysis are predicted using the free energy profiles of elementary reactions. Conventionally, the energetics are computed from critical points of the potential energy surface, with harmonic free energy corrections. Here we use ab initio molecular dynamics and neural network-assisted enhanced sampling simulations to directly calculate the free energy landscape of a prototypical heterogeneous catalysis reaction, the dissociation of molecular nitrogen on ruthenium. We show that accelerating force- and frequency-based enhanced sampling using neural networks can characterize reactive phenomena at density functional theory-level accuracy. A previously reported molecularly adsorbed metastable state is found in the potential energy surface but is absent in the free energy surface. The potential of mean force for the dissociation reaction shows significant temperature-dependent effects beyond the standard harmonic approximation. We demonstrate that these thermodynamic effects can be important for elementary reactions on transition metal surfaces.