As an AI language model, I cannot perform Density Functional Theory DFT calculations directly. However, I can guide you through the process of performing these calculations using appropriate software and methods.To calculate the activation energy for the reaction between methane and oxygen to form carbon dioxide and water using DFT, you will need to follow these steps:1. Choose a DFT software package: There are several DFT software packages available, such as Gaussian, VASP, Quantum Espresso, and ORCA. Choose one that you have access to and are familiar with.2. Build the molecular structures: Create the initial structures of the reactants methane and oxygen , the products carbon dioxide and water , and the transition state. You can use molecular modeling software like Avogadro, GaussView, or VMD to build and visualize the structures.3. Perform geometry optimization: Optimize the geometries of the reactants, products, and transition state using the chosen DFT software. This will provide you with the minimum energy structures for each species.4. Calculate the vibrational frequencies: Perform a frequency calculation for each optimized structure to ensure that you have found the correct stationary points on the potential energy surface. The reactants and products should have no imaginary frequencies, while the transition state should have exactly one imaginary frequency corresponding to the reaction coordinate.5. Determine the energy barriers: Compare the electronic energies of the transition state and the reactants. The difference in energy will give you the activation energy for the reaction.6. Include zero-point energy ZPE and thermal corrections: To obtain a more accurate activation energy, you should include the zero-point energy and thermal corrections to the electronic energies. These values can be obtained from the frequency calculations.7. Calculate the activation energy: The activation energy Ea can be calculated using the following equation:Ea = E_transition_state - E_reactants + ZPE_transition_state - ZPE_reactants + Thermal_correction_transition_state - Thermal_correction_reactants By following these steps, you can calculate the activation energy for the reaction between methane and oxygen to form carbon dioxide and water using density functional theory calculations.