Quantum cluster equilibrium theory applied to liquid ammonia.

Through this paper, the authors propose using the quantum cluster equilibrium (QCE) theory to reinvestigate ammonia clusters in the liquid phase. The ammonia clusters from size monomer to hexadecamer were considered to simulate the liquid ammonia in this approach. The clusterset used to model the liquid ammonia is an ensemble of different structures of ammonia clusters. After studious research of the representative configurations of ammonia clusters through the cluster research program ABCluster, the configurations have been optimized at the MN15/6-31++G(d,p) level of theory. These optimizations lead to geometries and frequencies as inputs for the Peacemaker code. The QCE study of this molecular system permits us to get the liquid phase populations in a temperature range of 190-260 K, covering the temperatures from the melting point to the boiling point. The results show that the population of liquid ammonia comprises mainly the ammonia hexadecamer followed by pentadecamer, tetradecamer, and tridecamer. We noted that the small-sized ammonia clusters do not contribute to the population of liquid ammonia. In addition, the thermodynamic properties, such as heat of vaporization, heat capacity, entropy, enthalpy, and free energies, obtained by the QCE theory have been compared to the experiment given some relatively good agreements in the gas phase and show considerable discrepancies in liquid phase except the density. Finally, based on the predicted population, we calculated the infrared spectrum of liquid ammonia at 215 K temperature. It comes out that the calculated infrared spectrum qualitatively agrees with the experiment.

Solvation energies of the ferrous ion in water and in ammonia at various temperatures.

CONTEXT: The solvation of metal ions is crucial to understanding relevant properties in physics, chemistry, or biology. Therefore, we present solvation enthalpies and solvation free energies of the ferrous ion in water and ammonia. Our results agree well with the experimental reports for the hydration free energy and hydration enthalpy. We obtained [Formula: see text] kJ mol[Formula: see text] for the hydration free energy and [Formula: see text] kJ mol[Formula: see text] for the hydration enthalpy of ferrous ion in water at room temperature. At ambient temperature, we obtained [Formula: see text] kJ mol[Formula: see text] as the [Formula: see text] ammoniation free energy and [Formula: see text] kJ mol[Formula: see text] for the ammoniation enthalpy. In addition, the free energy of solvation is deeply affected when the temperature increases. This pattern can be attributed to the rise of entropy when the temperature rises. Besides, the temperature does not affect the ammoniation enthalpies and the hydration enthalpy of the [Formula: see text] ion. METHOD: All the geometry optimizations are performed at the MP2 methods associated with the 6-31++g(d,p) basis set of Pople. solvated phase structures of [Formula: see text] ion in water or in ammonia are performed using the PCM model. The [Formula: see text] program suite was used to perform all the calculations. The program TEMPO was also used to evaluate the temperature sensitivity of the different obtained geometries.

Adsorption of some cationic dyes onto two models of graphene oxide.

CONTEXT: The search for highly efficient adsorbent materials remains a significant requirement in the field of adsorption for wastewater treatment. Computational study can highly contribute to the identification of efficient material. In this work, we propose a computational approach to study the adsorption of four cationic basic dyes, basic blue 26 (BB26), basic green 1 (BG1), basic yellow 2 (BY2), and basic red 1 (BR1), onto two models of graphene oxide as adsorbents. The main objectives of this study are the assessment of the adsorption capacity of the graphene oxide towards basic dyes and the evaluation of the environmental and temperature effects on the adsorption capacity. Quantum theory of atoms in molecules (QTAIM) analysis has been used to understand the interactions between the dyes and graphene oxides. In addition, adsorption free energies of the dyes onto graphene oxides are calculated in gas and solvent phases for temperatures varying from 200 to 400 K. As a result, the adsorption free energy varies linearly depending on the temperature, highlighting the importance of temperature effects in the adsorption processes. Furthermore, the results indicate that the environment (through the solvation) considerably affects the calculated adsorption free energies. Overall, the results show that the two models of graphene oxide used in this work are efficient for removing dyes from wastewater. METHODS: We have optimized the complexes formed by the interaction of dyes with graphene oxides at the PW6B95-D3/def2-SVP level of theory. The SMD solvation model realizes the implicit solvation, and water is used as the solvent. Calculations are performed using the Gaussian 16 suite of program. QTAIM analysis is performed using the AIMAll program. Gibbs free energies as function of temperature are calculated using the TEMPO program.

Exploration of the potential energy surfaces of small ethanol clusters.

The potential energy surfaces (PESs) of the ethanol clusters become increasingly complex as the cluster size increases. This is mainly due to the fact that there are up to three stable structures on the PES of the ethanol monomer yielding a huge number of possible structures of the ethanol clusters. In this work, we have thoroughly explored the PESs of neutral ethanol clusters from dimer to pentamer. For each cluster size, we have identified all possible combinations of the three monomers to build a structure of that cluster size. For each combination, we have used ABCluster to generate initial guessed geometries. These geometries have been fully optimized at the MP2/aug-cc-pVDZ level of theory. The results show that the PESs of the neutral ethanol clusters are symmetric due to enantiomerism of the clusters. For each cluster size, several isomers have been located as global minima energy structures. Globally, we have found that cyclic structures are the most stable, followed by branched cyclic and linear structures. The branched linear structures are found to be among the least stable structures on the PESs of the neutral ethanol clusters. The infrared spectra of the most stable structures are calculated and compared to experiment. The calculated infrared spectra are found to be in qualitative agreement with experiment. In addition, we have calculated the binding energies of the investigated ethanol clusters using MP2, some density functional theory (DFT) functionals (MN15, ωB97XD and PW6B95D3) and DLPNO-CCSD(T)/CBS levels of theory. As a result, we have found that the PW6B95D3 functional has the smallest mean absolute deviation (MAD) as compared to ωB97XD and MN15, when benchmarked to the DLPNO-CCSD(T)/CBS. Thus, we recommend the PW6B95D3 functional for affordable, yet accurate, exploration of neutral ethanol clusters.

Thermodynamic of solvation, solute - Solvent electron transfer and ionization potential of BSCAPE molecule and its UV-vis spectra in aqueous solution.

The molecular system 2-Phenylethyl (2E)-3-(1-benzenesulfonyl-4,5-dihydroxyphenyl) acrylate (BSCAPE) is a phenolic acid that covers a large spectrum of biological properties. The investigations of solvation and oxidation processes of BSCAPE molecule by computational means were the challenge of this present work. Water was required for solvation throughout the work. The explicit H2O were sequentially added to form the complexes BSCAPE(H2O)n=0-11. The discrete - continuum model was at the heart of this work. DFT and TD-DFT both associated to the continuum model SMD were required. Hence, the structures, the solvation energies, the energies of solute - solvent electron transfer (SSET), the ionisation potential (IP), and the UV-vis spectra were studied. It comes out that, the structure of the CAPE part included in BSCAPE agrees well with the available experimental values of CAPE but with a minor influence due to the presence of benzensulfonyl group. The enthalpy and free energy of solvation increase linearly with nH2O. The global reactivity indexes were assessed to appreciate the oxidation of BSCAPE. The latter quality was strongly assessed by the enthalpy and free energy of SSET and IP. The SSET potential increase with nH2O and the size of water clusters. The values 723.16 and 711.62 kJ/mol were found for enthalpy and free energy of IP respectively. Then in aqueous solution, the results fall down and upon addition of nH2O, they approach gas phase value for 11H2O and still are not stabilized. Therefore, the resistance to oxidation starts to raise at this level. Elsewhere, the UV-vis spectra of BSCAPE present four important peaks about 279.3, 234.8, 208.4 and 199.4 nm in gaseous state. The excitation shifts to the red as the number of H2O increase. Their oscillator strengths also increase with solvation.

Exploration of the potential energy surface of the ethanol hexamer.

The potential energy surfaces (PESs) of the neutral ethanol clusters is among the complex PESs of the neutral clusters. This is due to the fact that the ethanol monomer has three different isomers. In this work, we propose a systematic procedure to thoroughly explore the PES of the neutral ethanol hexamer that can be extended to other ethanol clusters. Thus, we started with a thorough exploration using the ABCluster code which uses the Lennard-Jones potential model. The resulting structures are further optimized at the APFD/6-31++g(d,p) level of theory {APFD refers to the initials of the first four authors in Austin et al. [J. Chem. Theory Comput. 8, 4989-5007 (2012)]}. Finally, 68 APFD structures have been fully re-optimized using the second order Møller-Plesset perturbation (MP2) method associated to the aug-cc-pVDZ basis set As a result, an isomer constituted of two trans ethanol monomers, two gauche+ ethanol monomers, and two gauche- ethanol monomers, is predicted to be the most stable structure using ABCluster. Full optimizations at the APFD/6-31++g(d,p) and MP2/aug-cc-pVDZ levels of theory confirm that this isomer is among the iso-energetic most stable structures of the ethanol hexamer. We found that most of the iso-energetic most stable structures are constituted of at least two different ethanol monomers. This highlights the importance of taking into account all the possible monomers in the exploration of the neutral ethanol clusters. In addition, we found that all the structures having their relative energies within 1.7 kcal mol-1 are cyclic structures. The results show that the most stable branched cyclic structures lies 1.7 kcal mol-1 above the most stable at the APFD/6-31++g(d,p) level of theory.

Structures, binding energies, temperature effects, infrared spectroscopy of [Mg(NH3 )n = 1-10 ]+ clusters from DFT and MP2 investigations.

The possible isomers of [Mg(NH3 )n = 1 - 10 ]+ clusters have been investigated using both M06-2X/6-31++G(d,p) and MP2/6-31++G(d,p) levels of theory. The isomeric distribution for each n size has been studied as a function of temperatures ranging from 25 to 400 K. To the best of our knowledge, for clusters size n > 6, this is the first theoretical study available in the literature. From the calculated values in the considered clusters and using a fitting procedure, we have evaluated the binding energies (-14.0 kcal/mol), clustering energies (-10.1 kcal/mol), clustering free energies (-2.8 kcal/mol), and clustering enthalpies (-10.3 kcal/mol). On the basis of our structural and infrared (IR) spectroscopy outcomes, we find that the first solvation shell can hold up to six ammonia molecules. © 2019 Wiley Periodicals, Inc.

Ionic radii of hydrated sodium cation from QTAIM.

The sodium cation is ubiquitous in aqueous chemistry and biological systems. Yet, in spite of numerous studies, the (average) distance between the sodium cation and its water ligands, and the corresponding ionic radii, are still controversial. Recent experimental values in solution are notably smaller than those from previous X-ray studies and ab initio molecular dynamics. Here we adopt a "bottom-up" approach of obtaining these distances from quantum chemistry calculations [full MP2 with the 6-31++G(d,p) and cc-pVTZ basis-sets] of gas-phase Na+(H2O)n clusters, as a function of the sodium coordination number (CN = 2-6). The bulk limit is obtained by the polarizable continuum model, which acts to increase the interatomic distances at small CN, but has a diminishing effect as the CN increases. This extends the CN dependence of the sodium-water distances from crystal structures (CN = 4-12) to lower CN values, revealing a switch between two power laws, having a small exponent at small CNs and a larger one at large CNs. We utilize Bader's theory of atoms in molecules to bisect the Na+-O distances into Na+ and water radii. Contrary to common wisdom, the water radius is not constant, decreasing even more than that of Na+ as the CN decreases. We also find that the electron density at the bond critical point increases exponentially as the sodium radius decreases.

Solvation energies of the proton in methanol revisited and temperature effects.

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 ΔGm(H+,T) = 0.200T - 1161.4.

Structures and spectroscopy of the ammonia eicosamer, (NH3)n=20.

In this work, we reported structures and relative stabilities of the neutral ammonia eicosamer at the APFD/6-31++g(d,p) level of theory. Furthermore, we have examined the temperature dependence isomer distribution and reported the relative population of the ammonia eicosamer for temperatures ranging from 20 to 400 K. Moreover, a theoretical infrared (IR) spectroscopic study is performed to confirm our results. As a result, several stable structures have been identified as isomers of the ammonia eicosamer. The most stable structure is a cage-like isomer with two central solvated ammonia molecules. It is found that cage-like isomers with central solvated ammonia molecules are more stable than other types of structures. Besides, two fused tetrameric cyclic structures belonging to the C2 symmetry point group are also located. Moreover, other reported isomers exhibit an amorphous behavior with no definite symmetry. When considering the temperature dependence isomer distribution, we found that only cage-like isomers contribute to the population of the ammonia eicosamer. The most stable isomer dominates the population of the cluster for all the investigated temperatures. Our analysis shows that only the IR spectra of isomers that contribute to the relative population have their peaks in agreement with the experiment. This agreement could be an indication of the reliability of our proposed structures of the ammonia eicosamer and their relative stability.

Structures and infrared spectroscopy of large sized protonated ammonia clusters.

We investigated in this work the structures and relative population of large sized protonated ammonia clusters, H + ( NH 3 ) n , n = 18, 20, 25, 30. To this end, we generated initial geometries using the ABCluster code. The 30 most stable geometries for each of the clusters have been fully optimized at the APFD/6-31++g(d,p) level of theory. The results show that the proton is asymmetrically shared by two ammonia molecules to form the NH 4 + ⋯ NH 3 complex. The NH 4 + ⋯ NH 3 complex occupies the center of the structures, and it is gradually solvated with increasing cluster size. For n = 25 and n = 30, the first solvation shell of NH 4 + ⋯ NH 3 is completely filled with some ammonia molecules present in the second solvation shell. Besides, we have reported the relative population of the investigated clusters at the thermodynamic equilibrium. As a result, the three most stable structures dominate the population of the clusters. For each cluster size, we found that the IR spectra of these three most stable structures are in agreement with experiments. This agreement could be an indication of the reliability of our investigations. Overall, the structures of large sized protonated ammonia clusters are cage-like and exhibit an amorphous behavior.

Structure, antioxidative potency and potential scavenging of OH and OOH of phenylethyl-3,4-dihydroxyhydrocinnamate in protic and aprotic media: DFT study.

DFT methods including B3LYP, B3PW91 and M05-2x associated to 6-31+G(d,p) were used for the structural and antioxidant potency studies of phenylethyl-3,4-dihydroxy-hydrocinnamate (PDH). Solvents were employed according to their protric and aprotic character. So, calculated structures agree with the experimental data. O4H4 is propitious to scavenge radicals whatever the medium except in water where O3H3 and O4H4 are competitive. The explicit solvents of dichloromethane (DCM) and water present a disparity of OH bond dissociation enthalpy and free energy (BDE and BDFE). These parameters are low in continuum except in water. The ionization potentials (IP) and potential affinities (PA) are low in solvents. BDE, IP and PA are each, approximatively constant in mixed solvent treatment in water using n-H2O (n=3,5,8). Elsewhere, H-atom transfer (HAT) mechanism is favoured in vacuum and DCM, whereas sequential proton loss electron transfer (SPLET) is likely in protic solvents. A discord between HAT and SPLET in benzene is observed. The PDH compound is more antioxidant and resistant to oxidation than caffeic acid phenethyl ester (CAPE). The potential of scavenging of OH and OOH whatever the reaction channel shows that they decay rapidly in any media through HAT. PDH is easily deprotonated in the protic solvents and the resulting product is the most antioxidant and the least resistant to oxidation.

Solvation energies of the proton in ammonia explicitly versus temperature.

We provide in this work, the absolute solvation enthalpies and the absolute solvation free energies of the proton in ammonia explicitly versus temperature. As a result, the absolute solvation free energy of the proton remains quite constant for temperatures below 200 K. Above this temperature, it increases as a linear function of the temperature: ΔGam(H+,T)=-1265.832+0.210 T. This indicates that a temperature change of 100 K would induce a solvation free energy change of 21 kJ mol-1. Thus, ignoring this free energy change would lead to a bad description of hydrogen bonds and an unacceptable error higher than 3.7 pKa units. However, the absolute solvation enthalpy of the proton in ammonia is not significantly affected by a temperature change and, the room temperature value is -1217 kJ mol-1. The change of the solvation enthalpy is only within 3 kJ mol-1 for a temperature change up to 200 K.

Structures and spectroscopy of medium size protonated ammonia clusters at different temperatures, H+(NH3)10-16.

Structures of protonated ammonia clusters (H+(NH3)n) are very important for the determination of pKa's and solvation energies of the proton in ammonia. In this work, their structures were investigated at M06-2X/6-31++g(d,p) level of theory, for n=10-16 and for temperatures ranging from 0 to 400 K. In the cluster community, this is the first theoretical study on the protonated ammonia clusters larger than the nonamer. We noted that the population of the investigated clusters is reproduced by branched cage or cage like structures at low temperatures, while branched linear and branched cyclic or branched double cyclic isomers are the only isomers responsible for the population at higher temperatures. In these isomers, the proton is highly and entirely solvated at the center of the cluster. In addition, protonated ammonia clusters are all Eigen structures and the first solvation shell of the related ammonium ion core is saturated by four ammonia molecules. Moreover, infrared (IR) spectra of all isomers have been investigated and these spectra show good agreement with the experiment. This allowed us to assign experimental peaks and to provide the constitution of the populations of the various clusters.

Structures and spectroscopy of protonated ammonia clusters at different temperatures.

The accurate determination of the solvation energies of a proton in ammonia is based on the precise knowledge of the structures of neutral and protonated ammonia clusters. In this work, we have investigated all the possible and stable structures of protonated ammonia clusters H+(NH3)n=2-9, along with their isomeric distribution at a specific temperature. New significant isomers are reported here for the first time and show that the structures of protonated ammonia clusters are not only branched linear as assumed by all previous authors. Branched linear structures are the only ones responsible for the population of protonated ammonia clusters for n = 4-6 at any temperature. However, for larger cluster sizes, these types of structures compete with branched cyclic, double cyclic, branched double cyclic and triple cyclic structures depending on the temperature. In addition, we have shown that protonated ammonia clusters are all Eigen structures and the first solvation shell of the related ammonium ion core is saturated by four ammonia molecules. We have also carried out a study of the hydrogen bond network of protonated ammonia clusters establishing the stability rule governing the various isomers of each cluster from estimated energies of the hydrogen bond types in H+(NH3)n=2-9. With all these results, a route for the accurate determination of the solvation energies of a proton in ammonia at a given temperature could be conceivable.

Structure and Spectroscopy of Hydrated Sodium Ions at Different Temperatures and the Cluster Stability Rules.

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.

Structures and relative stabilities of ammonia clusters at different temperatures: DFT vs. ab initio.

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.

DFT study of the effect of solvent on the H-atom transfer involved in the scavenging of the free radicals (·)HO2 and (·)O2(-) by caffeic acid phenethyl ester and some of its derivatives.

H-atom transfer from caffeic acid phenethyl ester (CAPE), MBC (3-methyl-2-butenyl caffeate), BC (benzoic caffeate), P3HC (phenethyl-3-hydroxycinnamate), and P4HC (phenethyl-4-hydroxycinnamate) to the selected free radicals (·)HO2 and (·)O2(-) was studied. Such a transfer can proceed in three different ways: concerted proton-coupled electron transfer (CPCET), electron transfer followed by proton transfer (ET-PT), and proton transfer followed by electron transfer (PT-ET). The latter pathway is sometimes competitive with SPLET (sequential proton loss electron transfer) in polar media. Analyzing the thermodynamic descriptors of the reactions of CAPE and its derivatives with co-reactive species-in particular, the free energies of reactions, the activation barrier to the CPCET mechanism, and their rate constants-appears to be the most realistic method of investigating the H-atom transfers of interest. These analyses were performed via DFT calculations, which agree well with the data acquired from experimental studies (IC50) and from CBS calculations. The CPCM solvation model was used throughout the work, while the SMD model-employed as a reference-was used only for CAPE. The main conclusion drawn from the analysis was that SPLET is the mechanism that governs the reaction of phenolic acids with (·)HO2, while PT-ET governs the reaction of phenols with (·)O2(-). In kinetic investigations of the CPCET process, the rate constant decreases as the solvent polarity increases, so the reaction velocity slows down.

Revision of the thermodynamics of the proton in gas phase.

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.

Structures of protonated methanol clusters and temperature effects.

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.