Elucidating the role of anharmonic effects in understanding oxidation of methane

In heterogeneous catalysis, materials property changes under operational environment (temperature (T), pressure (p)). Here we study T, p dependence of the composition, structure, and stability of metal oxide clusters using a relevant model system for practical applications: free transition metal (Ni) clusters in a combined oxygen and methane atmosphere. We have employed a robust methodological approach that integrates various levels of theory combined into one multi-scale simulation. To obtain the global minimum structures of the Ni₄O_x(CH₄)_y clusters, an extensive data set is generated using a massively parallel cascade genetic algorithm at the hybrid density functional level. The low energy clusters obtained from GA are further analysed to estimate their free energy of formation at realistic T, p_O2 and p_CH4.By analyzing this large dataset, we show that the conventional harmonic approximation miserably fails to predict thermodynamic stability and capturing the anharmonic effects to the vibration free energy contribution is indispensable. To include the anharmonic vibrational free energy to the configurational entropy, we evaluate the excess free energy of the clusters numerically by thermodynamic integration with ab initio molecular dynamics simulation inputs.