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Aiming towards materials design for methane activation, we study temperature($T$), pressure ($p$) dependence of the composition, structure, and stabilityof metal oxide clusters in a reactive atmosphere using a prototypical modelcatalyst having wide applications: free transition metal (Ni) clusters in acombined oxygen and methane atmosphere. A robust methodological approach isemployed, to show that the conventional harmonic approximation miserably failsfor this class of materials and capturing anharmonic effects to the vibrationfree energy contribution is indispensable. To incorporate the anharmonicity inthe vibrational free energy, we evaluate the excess free energy of the clustersnumerically by thermodynamic integration method with hybrid density functionaltheory and {\em ab initio} molecular dynamics simulation inputs. We find thatthe anharmonic effect has a significant impact in detecting the activation ofC$-$H bond, whereas the harmonic infrared spectrum completely fails due to thewrong prediction of the vibrational modes.

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