The activation energy of the C-H bond cleavage reaction in methane can be studied using quantum chemical calculations, such as density functional theory DFT or ab initio methods. These calculations provide insights into the potential energy surface PES of the reaction, which describes the energy of the system as a function of its molecular geometry.As the temperature increases, the kinetic energy of the molecules also increases, which can affect the activation energy of the C-H bond cleavage reaction. According to the Arrhenius equation, the rate constant k of a reaction is related to the activation energy Ea and temperature T as follows:k = Ae^-Ea/RT where A is the pre-exponential factor, R is the gas constant, and T is the temperature in Kelvin. As the temperature increases, the exponential term becomes less negative, leading to an increase in the rate constant.In the context of quantum chemical calculations, the activation energy can be determined by locating the transition state TS on the PES, which corresponds to the highest energy point along the reaction coordinate. The difference in energy between the TS and the reactants methane represents the activation energy for the C-H bond cleavage reaction.As the temperature increases, the increased kinetic energy of the molecules can lead to changes in the PES, such as a decrease in the energy barrier for the reaction or a change in the reaction pathway. This can result in a decrease in the activation energy for the C-H bond cleavage reaction, making the reaction more likely to occur at higher temperatures.In summary, the activation energy of the C-H bond cleavage reaction in methane can be affected by increasing temperature, as determined through quantum chemical calculations. Higher temperatures can lead to changes in the potential energy surface, resulting in a decrease in the activation energy and an increase in the rate constant for the reaction.