Proton transfer is ubiquitous in various physical/chemical processes, and the accurate determination of the thermodynamic parameters of the proton in the gas phase is useful for understanding and describing such reactions. However, the thermodynamic parameters of such a proton are usually determined by assuming the proton as a classical particle whatever the temperature. The reason for such an assumption is that the entropy of the quantum proton is not always soluble analytically at all temperatures. Thereby, we addressed this matter using a robust and reliable self-consistent iterative procedure based on the Fermi-Dirac formalism. As a result, the free proton gas can be assumed to be classical for temperatures higher than 200 K. However, it is worth mentioning that quantum effects on the gas phase proton motion are really significant at low temperatures (T ≤ 120 K). Although the proton behaves as a classical particle at high temperatures, we strongly recommend the use of quantum results at all temperatures, for the integrated heat capacity and the Gibbs free energy change. Therefore, on the basis of the thermochemical convention that ignores the proton spin, we recommend the following revised values for the integrated heat capacity and the Gibbs free energy change of the proton in gas phase and, at the standard pressure (1 bar): ΔH0→T = 6.1398 kJ mol(-1) and ΔG0→T = -26.3424 kJ mol(-1). Finally, it is important noting that the little change of the pressure from 1 bar to 1 atm affects notably the entropy and the Gibbs free energy change of the proton.

pKa's, proton affinities, and proton dissociation free energies characterize numerous properties of drugs and the antioxidant activity of some chemical compounds. Even with a higher computational level of theory, the uncertainty in the proton solvation free energy limits the accuracy of these parameters. We investigated the thermochemistry of the solvation of the proton in methanol within the cluster-continuum model. The scheme used involves up to nine explicit methanol molecules, using the IEF-PCM and the strategy based on thermodynamic cycles. All computations were performed at B3LYP/6-31++G(dp) and M062X/6-31++G(dp) levels of theory. It comes out from our calculations that the functional M062X is better than B3LYP, on the evaluation of gas phase clustering energies of protonated methanol clusters, per methanol stabilization of neutral methanol clusters and solvation energies of the proton in methanol. The solvation free energy and enthalpy of the proton in methanol were obtained after converging the partial solvation free energy of the proton in methanol and the clustering free energy of protonated methanol clusters, as the cluster size increases. Finally, the recommended values for the solvation free energy and enthalpy of the proton in methanol are -257 and -252 kcal/mol, respectively.

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