The global minimum energy structures of (NH ₃ ) _n=2–10 are pointed out for the first time at a given temperature.

The accurate evaluation of pKa’s, or solvation energies of the proton in methanol at a given temperature is subject to the determination of the most favored structures of various isomers of protonated (H+(MeOH)n) and neutral ((MeOH)n) methanol clusters in the gas phase and in methanol at that temperature. Solvation energies of the proton in a given medium, at a given temperature may help in the determination of proton affinities and proton dissociation energies related to the deprotonation process in that medium and at that temperature. pKa’s are related to numerous properties of drugs. In this work, we were interested in the determination of the most favored structures of various isomers of protonated methanol clusters in the gas phase and in methanol, at a given temperature. For this aim, the M062X/6-31++G(d,p) and B3LYP/6-31++G(d,p) levels of theory were used to perform geometries optimizations and frequency calculations on various isomers of (H+(MeOH)n) in both phases. Thermal effects were retrieved using our homemade FORTRAN code. Thus, we accessed the relative populations of various isomers of protonated methanol clusters, in both phases for temperatures ranging from 0 to 400 K. As results, in the gas phase, linear structures are entropically more favorable at high temperatures, while more compact ones are energetically more favorable at lower temperatures. The trend is somewhat different when bulk effects are taken into account. At high temperatures, the linear structure only dominates the population for n ⩽ 6, while it is dominated by the cyclic structure for larger cluster sizes. At lower temperatures, compact structures still dominate the population, but with an order different from the one established in the gas phase. Hence, temperature effects dominate solvent effects in small cluster sizes (n ⩽ 6), while the reverse trend is noted for larger cluster sizes.

We have revised the structures of neutral water clusters, (H ₂ O) _n=2–30 , with the affordable M06-2X functional, presenting up to 25 isomers for each cluster size.

We report in this work the absolute solvation enthalpies and the absolute solvation free energies of the proton in methanol at temperatures ranging from 20 to 340 K and an extrapolation to a desired temperature. To achieve this, we thoroughly investigated the structures of neutral methanol clusters (MeOH)_n=2–10 and those of the protonated methanol decamer H⁺(MeOH)_n=10 at the M06-2X/6-31++g(d,p) level of theory. As a result, we noted that up to the octamer, the population of the neutral methanol clusters is constituted by cyclic isomers. For nonamers and decamers, both cyclic and branched cyclic isomers contribute to the population of the clusters. Moreover, folded or distorted cyclic isomers are the most favored at low temperatures, while higher temperatures favored the flat cyclic isomers for n = 7–9. For the methanol decamer, a branched cyclic isomer is found to be the most favored at low temperatures. Elsewhere, the infrared spectra of all the investigated structures are provided and compared against experiment. The binding energy of neutral methanol is calculated at the X/6-31++g(d,p) levels of theory, where X represents the DFT functionals M062X, APFD, MN15, ωB97XD and M08HX. It is observed that these functionals provide results in good agreement with the experimental vaporization enthalpy. However, the APFD functional shows the best performance followed by the other functionals in the order of M062X, MN15 and ωB97XD. Furthermore, the calculated solvation energies of the proton in methanol at these various levels of theory and at MP2/6-31++g(d,p) show that the ωB97XD functional shows the best performance in evaluating the solvation enthalpy and the solvation free energy of the proton in methanol and the calculated values are respectively −1140.5 kJ mol⁻¹ and −1100.7 kJ mol⁻¹ at room temperature. Elsewhere, we noted that the absolute solvation enthalpy of the proton in methanol is less affected by a change in temperature. However, the absolute solvation free energy of the proton in methanol remains constant only at temperatures lower than 180 K. For higher temperatures, the absolute solvation free energy of the proton in methanol increases as a linear function of the temperature and can be approximated by ΔG_m(H⁺,T) = 0.200T − 1161.4.