As an AI language model, I cannot perform quantum chemistry calculations directly. However, I can guide you through the process of calculating the standard enthalpy of formation for methane gas using quantum chemistry calculations.1. Choose a quantum chemistry method: To perform quantum chemistry calculations, you need to choose a suitable method, such as Hartree-Fock HF , Density Functional Theory DFT , or post-Hartree-Fock methods like Mller-Plesset perturbation theory MP2 or Coupled Cluster CC . The choice of method depends on the desired accuracy and computational resources available.2. Select a basis set: A basis set is a mathematical representation of the atomic orbitals used in the calculations. Common basis sets include STO-3G, 6-31G, and cc-pVTZ. The choice of basis set affects the accuracy and computational cost of the calculations.3. Perform geometry optimization: Before calculating the enthalpy of formation, you need to find the equilibrium geometry of the molecule. This is done by minimizing the energy of the molecule with respect to its atomic positions using the chosen quantum chemistry method and basis set.4. Calculate the electronic energy: Once the equilibrium geometry is obtained, you can calculate the electronic energy of the molecule using the chosen quantum chemistry method and basis set.5. Calculate the zero-point vibrational energy ZPVE : The ZPVE is the lowest possible energy of a molecule due to its vibrational motion. This can be calculated using the vibrational frequencies obtained from a frequency analysis at the equilibrium geometry.6. Calculate the enthalpy: The enthalpy of the molecule can be calculated by adding the electronic energy, ZPVE, and the thermal corrections for the translational, rotational, and vibrational motions at the desired temperature usually 298.15 K .7. Calculate the standard enthalpy of formation: The standard enthalpy of formation Hf of methane can be calculated by subtracting the enthalpies of the isolated atoms in their standard states from the enthalpy of the methane molecule. For methane CH4 , this can be written as:Hf CH4 = H CH4 - [H C + 4 * H H ]After performing these calculations, you will obtain the standard enthalpy of formation for methane gas using quantum chemistry calculations. Keep in mind that the accuracy of the result depends on the chosen method and basis set.