The reaction between methane CH4 and chlorine Cl2 in the gas phase is a radical chain reaction, which can be described by the following steps:1. Initiation: Cl2 2Cl homolytic cleavage of the Cl-Cl bond 2. Propagation: a CH4 + Cl CH3 + HCl abstraction of a hydrogen atom from methane by a chlorine radical b CH3 + Cl2 CH3Cl + Cl reaction of the methyl radical with a chlorine molecule 3. Termination: Cl + Cl Cl2 or CH3 + Cl CH3Cl or CH3 + CH3 C2H6To predict the rate and mechanism of this reaction using a computational method in quantum chemistry, you can use the following steps:1. Choose an appropriate level of theory: Select a suitable quantum chemical method e.g., Density Functional Theory DFT , ab initio methods like Hartree-Fock HF , or post-Hartree-Fock methods like Mller-Plesset perturbation theory MP2 or Coupled Cluster CC and basis set e.g., 6-31G, 6-31G d , or cc-pVDZ based on the desired accuracy and computational cost.2. Optimize the geometry of reactants, products, and transition states: Perform geometry optimizations for CH4, Cl2, CH3, Cl, CH3Cl, and the transition states involved in the reaction. This will provide you with the most stable structures and their corresponding energies.3. Calculate the reaction energies and activation barriers: Compute the energy differences between the reactants, products, and transition states to determine the reaction energies and activation barriers for each step of the reaction.4. Estimate the rate constants: Use transition state theory TST or another suitable method to estimate the rate constants for each step of the reaction based on the calculated activation barriers and reaction energies.5. Determine the overall rate and mechanism: Analyze the rate constants for each step to determine the rate-determining step the slowest step and the overall rate of the reaction. The mechanism can be deduced from the sequence of elementary steps and their corresponding rate constants.Keep in mind that the accuracy of the predicted rate and mechanism depends on the chosen level of theory and the quality of the computational method used. Additionally, the reaction conditions e.g., temperature and pressure can also influence the rate and mechanism of the reaction.