As a language model AI, I cannot perform quantum chemical calculations directly. However, I can guide you on how to approach this problem.To calculate the binding energy of a non-covalent interaction between a water molecule H2O and a methane molecule CH4 , you would typically use a quantum chemistry method such as density functional theory DFT or a wavefunction-based method like Mller-Plesset perturbation theory MP2 or coupled-cluster theory CCSD T . These methods require specialized software like Gaussian, ORCA, or Psi4.Here's a general outline of the steps you would take:1. Choose a suitable level of theory: Select an appropriate method e.g., DFT, MP2, CCSD T and basis set e.g., 6-31G d , cc-pVDZ, aug-cc-pVDZ based on the accuracy you need and the computational resources available.2. Optimize the geometry: Perform a geometry optimization for the isolated water and methane molecules as well as for the water-methane complex. This will give you the minimum energy structures for each species.3. Calculate the single-point energies: Compute the single-point energies for the optimized structures of the isolated water, methane, and the water-methane complex.4. Calculate the binding energy: The binding energy is the difference between the energy of the water-methane complex and the sum of the energies of the isolated water and methane molecules:Binding energy = E H2O-CH4 - [E H2O + E CH4 ]Keep in mind that this is a simplified approach, and more advanced techniques such as counterpoise correction or basis set superposition error BSSE correction might be necessary to obtain more accurate results.To perform these calculations, you would need to use quantum chemistry software and have a good understanding of the methods and basis sets involved.