Theoretical Insights into C-H Bond Activation of Methane by Transition Metal Clusters: The Role of Anharmonic Effects

In heterogeneous catalysis, materials' property changes under operational conditions (i.e. temperature (T) and pressure (p) in an atmosphere of reactive molecules). Here we study T, p dependence of the composition, structure, and stability of metal oxide clusters using a prototypical model catalyst having practical applications: free transition metal (Ni) clusters in a combined oxygen and methane atmosphere. A robust methodological approach is employed, starting from systematic scanning of potential energy surface to obtain the global minimum structures using a massively parallel cascade genetic algorithm (cGA) at the hybrid density functional level. The low energy clusters are further analyzed to estimate their thermodynamic stability at realistic T, p_O2 and p_CH4 using ab initio atomistic thermodynamics. To incorporate the anharmonicity in the vibrational free energy contribution to the configurational entropy, we evaluate the excess free energy of the clusters numerically by thermodynamic integration method with ab initio molecular dynamics (aiMD) simulation inputs. By analyzing a large dataset, we show that the conventional harmonic approximation miserably fails for this class of materials and capturing anharmonic effects is significant in detecting the activation of C-H bond.