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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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.

A hydrogen bond network in ammonia clusters plays a key role in understanding the properties of species embedded in ammonia. This network is dictated by the structures of neutral ammonia clusters. In this work, structures of neutral ammonia clusters (NH3)n(=2-10) have been studied at M06-2X/6-31++G(d,p) and MP2/6-31++g(d,p) levels of theory. The analysis of the relative stabilities of various hydrogen bond types has also been studied and vibrational spectroscopy of the ammonia pentamer and decamer is investigated. We noted that M06-2X provides lower electronic energies, greater binding energies and higher structural resolution than MP2. We also noted that at the M06-2X level of theory, the binding energy converges to the experimental vaporization enthalpy faster than that at the MP2 level of theory. As a result, it is found that the M06-2X functional could be more suitable than the MP2 ab initio method in the description of structures and energies of ammonia clusters. However, we found that the electronic energy differences obtained at both levels of computation follow a linear relation with n (number of ammonia molecules in a cluster). As far as the structures of ammonia clusters are concerned, we proposed new "significant" isomers that have not been reported previously. The most remarkable is the global minimum electronic energy structure of the ammonia hexamer, which has an inversion centre and confirms experimental observation. Moreover, we reported the relative stabilities of neutral ammonia clusters for temperatures ranging from 25 to 400 K. The stability of isomers changes with the increase of the temperature. As a result, the branched and less bonded isomers are the most favored at high temperatures and disfavored at low temperatures, while compact and symmetric isomers dominate the population of clusters at low temperatures. In fine, from this work, the global minimum energy structures of ammonia clusters are known for the first time at a given temperature (T ∼ 0-400 K) and at a reliable computational level of theory.

We have revised the structures of neutral water clusters, (H2O)n=2–30, with the affordable M06-2X functional, presenting up to 25 isomers for each cluster size.

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The sodium cation plays an important role in several physiological processes. Understanding its solvation may help understanding ion selectivity in sodium channels that are pivotal for nerve impulses. This paper presents a thorough investigation of over 75 isomers of gas-phase Na(+)(H2O)(n=1-8) clusters, whose optimized structures, energies, and (harmonic) vibrational frequencies were computed quantum mechanically at the full MP2/6-31++G(d,p) level of theory. From these data, we have calculated the temperature effects on the cluster thermodynamic functions, and thus the equilibrium Boltzmann distribution for each n. For a selected number of isomers, we have corrected the calculations for basis set superposition error (BSSE) to obtain accurate clustering energies, in excellent agreement with experiment. The computed clusters are overwhelmingly 4-coordinated, as opposed to bulk liquid water, where sodium cations are believed to be mostly 5- or 6-coordinated. To explain this, we suggest the "cluster stability rules", a set of coordination-number-dependent hydrogen-bond (HB) strengths that can be obtained using a single BSSE correction. Assuming additivity and transferability, these reproduce the relative stability of most of our computed isomers. These rules enable us to elucidate the trends in HB strengths, outlining the major determinants of cluster stability. For n = 4 and 5, we have also performed anharmonic vibrational calculations (VPT2) to compare with available photodissociation infrared spectra of these gas-phase clusters. The comparison suggests that the experiments actually monitor a mixture of predominantly 3-coordinated isomers, which is quite remote from the computed Boltzmann distribution, particularly at low temperatures. Surprisingly, for these experiments, water evaporation pathways can rationalize the non-equilibrium isomer distribution. The equilibrium isomer distribution is, in turn, rationalized by the entropy of internal rotations of "dangling" water molecules.