Calculational method for investigation thermodynamic properties of water, methanol, and water-methanol mixtures

Three quantum chemical methods, namely B3LYP, MP2, and coupled-cluster singles and doubles (CCSD), were employed to investigate the temperature dependence of the thermodynamic properties of water, methanol, and their mixtures in both the gas and solution phases. The thermodynamic state functions, including Gibbs free energy, enthalpy, and internal energy, of water, methanol, and a water–methanol mixture with a methanol mole fraction of 0.50 were calculated over a range of temperatures. Solvent effects were incorporated using the Integral Equation Formalism Polarizable Continuum Model (IEFPCM). The calculated Gibbs free energies obtained with the B3LYP method exhibited noticeable deviations from those predicted by the higher-level ab initio methods (MP2 and CCSD), which may be attributed to the approximate treatment of exchange–correlation effects in the density functional. In contrast, the CCSD method provides a more rigorous description of electron correlation through the correlated many-electron wave function. The difference between the MP2 and B3LYP results is greater than the difference between the MP2 and CCSD results for the enthalpy of the methanol solution. It is also worth noting that the use of larger basis sets, such as 6-31G(d) and 6-31G(d,p), does not significantly affect thermodynamic properties, including the enthalpy of methanol. Similarly, the enthalpy of methanol in solution showed method-dependent temperature behavior, reflecting differences in the theoretical treatment of electron correlation. The mixing enthalpy of the water–methanol solution at a methanol mole fraction of 0.50 was further evaluated using the CCSD method. The results indicate that the mixing enthalpy increases monotonically with temperature, and the calculated values are in good agreement with the available experimental data, demonstrating that the coupled-cluster approach provides a reliable description of the thermodynamic properties of water–methanol mixtures.