Rice–Ramsperger–Kassel–Marcus Simulation of Hydrogen Dissociation on Cu(111): Addressing Dynamical Biases, Surface Temperature, and Tunneling

Abstract

The effects of dynamics, surface temperature, and tunneling on the dissociative chemisorption of hydrogen on Cu(111) are explored using a dynamically biased precursor-mediated microcanonical trapping (d-PMMT) model. Transition state vibrational frequencies were taken from recent generalized gradient approximation density functional theory (GGA-DFT) electronic structure calculations, and the model’s few remaining parameters were fixed by optimizing simulations to a limited number of quantum-state-resolved associative desorption experiments. The d-PMMT model reproduces a diverse variety of dissociative chemisorption and associative desorption experimental results and, importantly, largely captures the surface temperature dependence of quantum-state-resolved dissociative sticking coefficients. Molecular translational energy parallel to the surface was treated as a spectator degree of freedom. The efficacy of molecular rotational energy to promote dissociation, relative to normal translational energy, varied monotonically from −45% to 33% as the rotational energy increased. Efficacies for molecular vibrational energy and surface phonon energy were 60%. The efficacies did not vary with isotope change from H₂ to D₂. The thermal dissociative sticking coefficient for H₂/Cu­(111) is predicted to vary as <i>S</i>(<i>T</i>) = <i>S</i>₀ exp­(−<i>E</i>_a/<i>RT</i>) where <i>S</i>₀ = 0.075 and <i>E</i>_a = 49.2 kJ/mol over the 300 K ≤ <i>T</i> ≤ 1000 K temperature range. Dynamical effects are significant and suppress <i>S</i>(<i>T</i>) by ∼2 orders of magnitude as compared to statistical expectations. For thermal dissociative chemisorption of H₂/Cu­(111) at 1000 K, a temperature of catalytic interest, normal translational energy is calculated to provide 57% of the energy necessary to react, surface phonons 23%, molecular rotation 15%, and vibration 5%. Tunneling is calculated to account for 13% of <i>S</i>(<i>T</i>) at 1000 K and more than 50% at temperatures below 400 K. These results demonstrate that many aspects of gas-surface reactivity can be modeled using microcanonical transition state theory subject to a few dynamical constraints