Single-ion solvation free energies and the normal hydrogen electrode potential in methanol, acetonitrile, and dimethyl sulfoxide

The division of thermodynamic solvation free energies of electrolytes into contributions from individual ionic constituents is conventionally accomplished by using the single-ion solvation free energy of one reference ion, conventionally the proton, to set the single-ion scales. Thus, the determination of the free energy of solvation of the proton in various solvents is a fundamental issue of central importance in solution chemistry. In the present article, relative solvation free energies of ions and ion-solvent clusters in methanol, acetonitrile, and dimethyl sulfoxide (DMSO) have been determined using a combination of experimental and theoretical gas-phase free energies of formation, solution-phase reduction potentials and acid dissociation constants, and gas-phase clustering free energies. Applying the cluster pair approximation to differences between these relative solvation free energies leads to values of -263.5, -260.2, and -273.3 kcal/mol for the absolute solvation free energy of the proton in methanol, acetonitrile, and DMSO, respectively. The final absolute proton solvation free energies are used to assign absolute values for the normal hydrogen electrode potential and the solvation free energies of other single ions in the solvents mentioned above.     

Modeling protic to dipolar aprotic solvent rate acceleration and leaving group effects in S(N)2 reactions: A theoretical study of the reaction of acetate ion with ethyl halides in aqueous and dimethyl sulfoxide solutions

The S(N)2 reactions between acetate ions and ethyl chloride, ethyl bromide, and ethyl iodide in aqueous and dimethyl sulfoxide (DMSO) solutions were theoretically investigated at an ab initio second-order M?ller-Plesset perturbation level of theory for geometry optimizations and at a fourth-order M?ller-Plesset perturbation level for energy calculations. The solvent effect was included by the polarizable continuum model using the Pliego and Riveros parametrization for DMSO and the Luque et al. scale factor for the water solution. The calculated DeltaG() values of 24.9, 20.0, and 18.5 kcal mol(-1) in a DMSO solution for ethyl chloride, ethyl bromide, and ethyl iodide are in good agreement with the estimated experimental values of 22.3, 20.0, and 16.6 kcal mol(-1), respectively. In an aqueous solution, the theoretical Delta G++ barriers of 26.9, 23.1, and 22.1 kcal mol(-1) are also in good agreement with the estimated experimental values of 26.1, 25.2, and 24.7 kcal mol(-1), respectively. The present ab initio calculations are reliable to predict the absolute and relative reactivities of ethyl halides in a DMSO solution, but in the aqueous phase, the results are less accurate. The protic to dipolar aprotic solvent rate acceleration is theoretically predicted, although this effect is underestimated. We suggest that further improvement of the present results could be obtained by including liquid-phase optimization in both solvents and treating specific solvation by water molecules for the reaction in the aqueous phase.     

Proton solvation in protic and aprotic solvents

Protonation pattern strongly affects the properties of molecular systems. To determine protonation equilibria, proton solvation free energy, which is a central quantity in solution chemistry, needs to be known. In this study, proton affinities (PAs), electrostatic energies of solvation, and pK_A values were computed in protic and aprotic solvents. The proton solvation energy in acetonitrile (MeCN), methanol (MeOH), water, and dimethyl sulfoxide (DMSO) was determined from computed and measured pK_A values for a specially selected set of organic compounds. pK_A values were computed with high accuracy using a combination of quantum chemical and electrostatic approaches. Quantum chemical density functional theory computations were performed evaluating PA in the gas‐phase. The electrostatic contributions of solvation were computed solving the Poisson equation. The computations yield proton solvation free energies with high accuracy, which are in MeCN, MeOH, water, and DMSO ?255.1, ?265.9, ?266.3, and ?266.4 kcal/mol, respectively, where the value for water is close to the consensus value of ?265.9 kcal/mol. The pK_A values of MeCN, MeOH, and DMSO in water correlates well with the corresponding proton solvation energies in these liquids, indicating that the solvated proton was attached to a single solvent molecule. © 2016 Wiley Periodicals, Inc.     

Aqueous solvation free energies of ions and ion-water clusters based on an accurate value for the absolute aqueous solvation free energy of the proton

Thermochemical cycles that involve pKa, gas-phase acidities, aqueous solvation free energies of neutral species, and gas-phase clustering free energies have been used with the cluster pair approximation to determine the absolute aqueous solvation free energy of the proton. The best value obtained in this work is in good agreement with the value reported by Tissandier et al. (Tissandier, M. D.; Cowen, K. A.; Feng, W. Y.; Gundlach, E.; Cohen, M. J.; Earhart, A. D.; Coe, J. V. J. Phys. Chem. A 1998, 102, 7787), who applied the cluster pair approximation to a less diverse and smaller data set of ions. We agree with previous workers who advocated the value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton. Considering the uncertainties associated with the experimental gas-phase free energies of ions that are required to use the cluster pair approximation as well as analyses of various subsets of data, we estimate an uncertainty for the absolute aqueous solvation free energy of the proton of no less than 2 kcal/mol. Using a value of -265.9 kcal/mol for the absolute aqueous solvation free energy of the proton, we expand and update our previous compilation of absolute aqueous solvation free energies; this new data set contains conventional and absolute aqueous solvation free energies for 121 unclustered ions (not including the proton) and 147 conventional and absolute aqueous solvation free energies for 51 clustered ions containing from 1 to 6 water molecules. When tested against the same set of ions that was recently used to develop the SM6 continuum solvation model, SM6 retains its previously determined high accuracy; indeed, in most cases the mean unsigned error improves when it is tested against the more accurate reference data.     

Calculation of the solvation free energy of neutral and ionic molecules in diverse solvents

The solvation free energy density (SFED) model was modified to extend its applicability and predictability. The parametrization process was performed with a large, diverse set of solvation free energies that included highly polar and ionic molecules. The mean absolute error for 1200 solvation free energies of the 379 neutral molecules in 9 organic solvents and water was 0.40 kcal/mol, and for 90 hydration free energies of ions was 1.7 kcal/mol. Overall, the calculated solvation free energies of a wide range of solute functional groups in diverse solvents were consistent with experimental data.     

温度对二甲基亚砜水溶液的结构和热力学性质的影响

应用参考作用格位模型理论计算了二甲基亚砜(DMSO)摩尔分数为0.002时不同温度下溶液的微观结构和热力学性质. 计算结果表明, DMSO加入到水中能够增强溶液的分子网络结构. 温度升高, 配位数减小, 溶液中分子排布趋向无序. 平均力势的波动增大表明分子间的诱导力表现为斥力. 计算得到的各种热力学性质显示: 温度升高, 溶液的熵和溶剂化自由能增加, 相互作用能和过剩化学位也增加, 即高温下溶液越来越偏离理想溶液; 空位形成能降低表明溶液分子结构在高温下更容易重组.     

Gas-Phase and Solution-Phase Homolytic Bond Dissociation Energies of H-N(+) Bonds in the Conjugate Acids of Nitrogen Bases

The oxidation potentials of 19 nitrogen bases (abbreviated as B: six primary amines, five secondary amines, two tertiary amines, three anilines, pyridine, quinuclidine, and 1,4-diazabicyclo[2,2,2]octane), i.e., E(ox)(B) values in dimethyl sulfoxide (DMSO) and/or acetonitrile (AN), have been measured. Combination of these E(ox)(B) values with the acidity values of the corresponding acids (pK(HB)(+)) in DMSO and/or AN using the equation: BDE(HB)(+) = 1.37pK(HB)(+) + 23.1 E(ox)(B) + C (C equals 59.5 kcal/mol in AN and 73.3 kcal/mol in DMSO) gave estimates of solution phase homolytic bond dissociation energies of H-B(+) bonds. Gas-phase BDE values of H-B(+) bonds were estimated from updated proton affinities (PA) and adiabatic ionization potentials (aIP) using the equation, BDE(HB(+))(g) = PA + aIP - 314 kcal/mol. The BDE(HB)(+) values estimated in AN were found to be 5-11 kcal/mol higher than the corresponding gas phase BDE(HB(+))(g) values. These bond-strengthening effects in solution are interpreted as being due to the greater solvation energy of the HB(+) cation than that of the B(+*) radical cation.     

Confusing cause and effect: energy-entropy compensation in the preferential solvation of a nonpolar solute in dimethyl sulfoxide/water mixtures

We performed molecular simulations to analyze the thermodynamics of methane solvation in dimethyl sulfoxide (DMSO)/water mixtures (298 K, 1 atm). Two contributions to the interaction thermodynamics are studied separately: (i) the introduction of solute-solvent interactions (primary contribution) and (ii) the solute-induced disruption of cohesive solvent-solvent interactions (secondary contribution). The energy and entropy changes of the secondary contribution always exactly cancel in the free energy (energy-entropy compensation), hence only the primary contribution is important for understanding changes of the free energy. We analyze the physical significance of the solute-solvent energy and solute-solvent entropy associated with the primary contribution and discuss how to obtain these quantities from experiments combining solvation thermodynamic and solvent equation of state data. We show that the secondary contribution dominates changes in the methane solvation entropy and enthalpy: below 30 mol % DMSO in the mixture, methane, because of more favorable dispersion interactions with DMSO molecules, preferentially attracts DMSO molecules, which, in response, release water molecules into the bulk, causing an increase in the entropy. This large energy-entropy compensating process easily causes a confusion in the cause for and the effect of preferred methane-DMSO interactions. Methane-DMSO dispersion interactions are the cause, and the entropy change is the effect. Procedures that infer thermodynamic driving forces from analyses of the solvation entropies and enthalpies should therefore be used with caution.     

A novel quantum mechanical/molecular mechanical approach to the free energy calculation for isomerization of glycine in aqueous solution

The free energy change associated with the isomerization reaction of glycine in water solution has been studied by a hybrid quantum mechanical/molecular mechanical (QM/MM) approach combined with the theory of energy representation (QM/MM-ER) recently developed. The solvation free energies for both neutral and zwitterionic form of glycine have been determined by means of the QM/MM-ER simulation. The contributions of the electronic polarization and the fluctuation of the QM solute to the solvation free energy have been investigated. It has been found that the contribution of the density fluctuation of the zwitterionic solute is estimated as -4.2 kcal/mol in the total solvation free energy of -46.1 kcal/mol, while that of the neutral form is computed as -3.0 kcal/mol in the solvation free energy of -15.6 kcal/mol. The resultant free energy change associated with the isomerization of glycine in water has been obtained as -7.8 kcal/mol, in excellent agreement with the experimental data of -7.3 or -7.7 kcal/mol, implying the accuracy of the QM/MM-ER approach. The results have also been compared with those computed by other methodologies such as the polarizable continuum model and the classical molecular simulation. The efficiency and advantage of the QM/MM-ER method has been discussed.     

1H NMR, 13C NMR, and computational DFT studies of the structure of 2-acylcyclohexane-1,3-diones and their alkali metal salts in solution

1H and 13C NMR spectra of 2-acyl-substituted cyclohexane-1,3-diones (acyl = formyl, 1; 2-nitrobenzoyl, 2; 2-nitro-4-trifluoromethylbenzoyl, 3) and lithium sodium and potassium salts of 1 have been measured. The compound 3, known as NTBC, is a life-saving medicine applied in tyrosinemia type I. The optimum molecular structures of the investigated objects in solutions have been found using the DFT method with B3LYP functional and 6-31G** and/or 6-311G(2d,p) basis set. The theoretical values of the NMR parameters of the investigated compounds have been calculated using GIAO DFT B3LYP/6-311G(2d,p) method. The theoretical data obtained for compounds 1-3 have been exploited to interpret their experimental NMR spectra in terms of the equilibrium between different tautomers. It has been found that for these triketones an endo-tautomer prevails. The differences in NMR spectra of the salts of 1 can be rationalized taking into account the size of the cation and the degree of salt dissociation. It seems that in DMSO solution the lithium salt exists mainly as an ion pair stabilized by the chelation of a lithium cation with two oxygen atoms. The activation free energy the of formyl group rotation for this salt has been estimated to be 51.5 kJ/mol. The obtained results suggest that in all the investigated objects, including the free enolate ions, all atoms directly bonded to the carbonyl carbons lie near the same plane. Some observations concerning the chemical shift changes could indicate strong solvation of the anion of 1 by water molecules. Implications of the results obtained in this work for the inhibition mechanism of (4-hydroxyphenyl) pyruvate dioxygenase by NTBC are commented upon.     

Free energy of solvation of simple ions: molecular-dynamics study of solvation of Cl- and Na+ in the ice/water interface

Molecular-dynamics simulations of Cl(-) and Na(+) ions are performed to calculate ionic solvation free energies in both bulk simple point-charge/extended water and ice 1 h at several different temperatures, and at the basal ice 1 h/water interface. For the interface we calculate the free energy of "transfer" of the ions across the ice/water interface. For the ions in bulk water in the NPT ensemble at 298 K and 1 atm, results are found to be in good agreement with experiments, and with other simulation results. Simulations performed in the NVT ensemble are shown to give equivalent solvation free energies, and this ensemble is used for the interfacial simulations. Solvation free energies of Cl(-) and Na(+) ions in ice at 150 K are found to be approximately 30 and approximately 20 kcal mol(-1), respectively, less favorable than for water at room temperature. Near the melting point of the model the solvation of the ions in water is the same (within statistical error) as that measured at room temperature, and in the ice is equivalent and approximately 10 kcal mol(-1) less favorable than the liquid. The free energy of transfer for each ion across ice/water interface is calculated and is in good agreement with the bulk observations for the Cl(-) ion. However, for the model of Na(+) the long-range electrostatic contribution to the free energy was more negative in the ice than the liquid, in contrast with the results observed in the bulk calculations.     

Anisotropic solvent model of the lipid bilayer. 1. Parameterization of long-range electrostatics and first solvation shell effects

A new implicit solvation model was developed for calculating free energies of transfer of molecules from water to any solvent with defined bulk properties. The transfer energy was calculated as a sum of the first solvation shell energy and the long-range electrostatic contribution. The first term was proportional to solvent accessible surface area and solvation parameters (σ(i)) for different atom types. The electrostatic term was computed as a product of group dipole moments and dipolar solvation parameter (η) for neutral molecules or using a modified Born equation for ions. The regression coefficients in linear dependencies of solvation parameters σ(i) and η on dielectric constant, solvatochromic polarizability parameter π*, and hydrogen-bonding donor and acceptor capacities of solvents were optimized using 1269 experimental transfer energies from 19 organic solvents to water. The root-mean-square errors for neutral compounds and ions were 0.82 and 1.61 kcal/mol, respectively. Quantification of energy components demonstrates the dominant roles of hydrophobic effect for nonpolar atoms and of hydrogen-bonding for polar atoms. The estimated first solvation shell energy outweighs the long-range electrostatics for most compounds including ions. The simplicity and computational efficiency of the model allows its application for modeling of macromolecules in anisotropic environments, such as biological membranes.     

Accurate pK(a) calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods

Complete Basis Set and Gaussian-n methods were combined with CPCM continuum solvation methods to calculate pK(a) values for six carboxylic acids. An experimental value of -264.61 kcal/mol for the free energy of solvation of H(+), DeltaG(s)(H(+)), was combined with a value for G(gas)(H(+)) of -6.28 kcal/mol to calculate pK(a) values with Cycle 1. The Complete Basis Set gas-phase methods used to calculate gas-phase free energies are very accurate, with mean unsigned errors of 0.3 kcal/mol and standard deviations of 0.4 kcal/mol. The CPCM solvation calculations used to calculate condensed-phase free energies are slightly less accurate than the gas-phase models, and the best method has a mean unsigned error and standard deviation of 0.4 and 0.5 kcal/mol, respectively. The use of Cycle 1 and the Complete Basis Set models combined with the CPCM solvation methods yielded pK(a) values accurate to less than half a pK(a) unit.     

Solvent effects on methyl transfer reactions. 2. The reaction of amines with trimethylsulfonium salts.

The reaction of ammonia and pyridine with trimethylsulfonium ion has been studied in gas phase and solution. Density functional theory at the B3LYP/6-31+G level was used to describe the energy changes along the reaction coordinate in the gas phase, and the self-consistent isodensity polarizable continuum model (SCI-PCM) was used to calculate the effect of cyclohexane and dimethyl sulfoxide as the solvent on the energy changes. The effect of water as the solvent was studied using the Monte Carlo free energy perturbation method. The reaction with both ammonia and pyridine follows a similar rather convoluted path in gas phase, with the formation of several reaction complexes before and after the formation of the transition state. All the species found in gas phase persist in cyclohexane, yielding a reaction path very similar to that in gas phase but with significant differences in the relative energy of the critical points. In DMSO, the energy profile is greatly simplified by the disappearance of several of the species found in gas phase and in cyclohexane. The activation free energy increases with the polarity of the solvent in both reactions. Increasing the polarity of the solvent also increases the exothermicity of the reaction of trimethylsulfonium ion with ammonia and reduces it in the reaction with pyridine. In water, the free energy profile follows the same trend as found for DMSO, and free energy of activation is calculated to be larger by about 2-3 kcal/mol. This is in good agreement with an experimental measurement of the effect of solvent on the rate of reaction.     

Theoretical studies of the tautomeric equilibria for five-member N-heterocycles in the gas phase and in solution

Tautomeric equilibria have been studied for five-member N-heterocycles and their methyl derivatives in the gas phase and in different solvents with dielectric constants of epsilon = 4.7-78.4. The free energy changes differently for tautomers upon solvation as compared to the gas phase, resulting in a shift of the equilibrium constant in solution. Solvents with increasing dielectric constant produce more negative solute-solvent interaction energies and increasing internal energies. The methyl-substituted imidazole and pyrrazole form delicate equilibria between two tautomeric forms. Depending on the solvent, the methyl-substituted triazoles and tetrazole have one or two major tautomers in solution. When estimating the relative solvation free energies by means of an explicit solvent model and using the FEP/MC method, one observes that the preferred tautomers differ in several cases from those predicted by the continuum solvent model. The 1,2-prototropic shift, as an intramolecular tautomerization path, requires about 50 kcal/mol activation energy for imidazole in the gas phase, and this route is also disfavored in a solution. The calculated activation free energy along the intramolecular path is 48-50 kcal/mol in chloroform and water as compared to a literature value of 13.6 kcal/mol for pyrrazole in DMSO. A molecular dynamics computer experiment favors the formation of an imidazole chain in chloroform, making the 1,3-tautomerization feasible along an intermolecular path in nonprotic solvents. In aqueous solution, one strong N-H...Ow hydrogen bond is formed for each species, whereas all other nitrogens in the ring form weaker, N...HwOw type hydrogen bonds. The tetrahydrofuran solvent acts as a hydrogen bond acceptor and forms N-H...Oether bonds. Molecules of the dichloromethane solvent are in favorable dipole-dipole interactions with the solute. The results obtained are useful in the design of N-heterocyclic ligands forming specified hydrogen bonds with protein side chains.     

A reliable and efficient first principles-based method for predicting pKa values. III. Adding explicit water molecules: Can the theoretical slope be reproduced and pKa values predicted more accurately?

A popular method for predicting pK(a) values for organic molecules in aqueous solution is to establish empirical linear least-squares fits between calculated deprotonation energies and known experimental pK(a) values. In virtually all such calculations, the empirically observed slope of the pK(a) vs. ΔE fit is significantly less than the theoretical value, 1/(2.303RT) (which is 0.73 mol/kcal at room temperature). In our own continuum solvation calculations (Zhang et al., J Phys Chem A 2010, 114, 432), the empirical slope for carboxylic acids was only 0.23 mol/kcal, despite the excellent fit to the experimental pK(a) values. There has been much speculation about the reason for this phenomenon. Although the ΔE - pK(a) relation neglects entropic effects, these are expected to largely cancel. The most likely cause for the strange behavior of the fitted slope is explicit solute-solvent (water) interactions, especially involving the ions, which cannot be described accurately by continuum solvation models. We used our previously developed pK(a) protocol (OLYP/6-311+G(d,p)//3-21G(d) with the COSMO solvation model) to investigate the effect of adding one or two explicit water molecules to the system. The slopes for organic acids (especially carboxylic acids) are much closer to the theoretical value when explicit water molecules are added to both the neutral molecule and the anion. However, explicit water molecules have almost no effect on the slopes for organic bases. Adding explicit water molecules to the ions only produces intermediate results. Unfortunately, linear fits involving explicit water molecules have much larger errors than with continuum solvation models alone and are also much more expensive. Consequently, they are not suitable for large-scale pK(a) calculations. The results compared with literature values showed that our predicted pK(a) s are more accurate.     

Calculation of solvation free energies of charged solutes using mixed cluster/continuum models

We derive a consistent approach for predicting the solvation free energies of charged solutes in the presence of implicit and explicit solvents. We find that some published methodologies make systematic errors in the computed free energies because of the incorrect accounting of the standard state corrections for water molecules or water clusters present in the thermodynamic cycle. This problem can be avoided by using the same standard state for each species involved in the reaction under consideration. We analyze two different thermodynamic cycles for calculating the solvation free energies of ionic solutes: (1) the cluster cycle with an n water cluster as a reagent and (2) the monomer cycle with n distinct water molecules as reagents. The use of the cluster cycle gives solvation free energies that are in excellent agreement with the experimental values obtained from studies of ion-water clusters. The mean absolute errors are 0.8 kcal/mol for H(+) and 2.0 kcal/mol for Cu(2+). Conversely, calculations using the monomer cycle lead to mean absolute errors that are >10 kcal/mol for H(+) and >30 kcal/mol for Cu(2+). The presence of hydrogen-bonded clusters of similar size on the left- and right-hand sides of the reaction cycle results in the cancellation of the systematic errors in the calculated free energies. Using the cluster cycle with 1 solvation shell leads to errors of 5 kcal/mol for H(+) (6 waters) and 27 kcal/mol for Cu(2+) (6 waters), whereas using 2 solvation shells leads to accuracies of 2 kcal/mol for Cu(2+) (18 waters) and 1 kcal/mol for H(+) (10 waters).     

On the mechanisms of oxidation of organic sulfides by H2O2 in aqueous solutions

The mechanism of oxidation of organic sulfides in aqueous solutions by hydrogen peroxide was investigated via ab initio calculations. Specifically, two reactions, hydrogen transfer of hydrogen peroxide to form water oxide and the oxidation of dimethyl sulfide (DMS) by hydrogen peroxide to form dimethyl sulfoxide, were studied as models of these processes in general. Solvent effects are included both via including explicitly water molecules and via the polarizable continuum model. The former was found to have a much more significant effect than the latter. When explicit water molecules are included, a mechanism different from those proposed in the literature was found. Specific interactions including hydrogen bonding with 2-3 water molecules can provide enough stabilization for the charge separation of the activation complex. The energy barrier of the oxidation of DMS by hydrogen peroxide was estimated to be 12.7 kcal/mol, within the experimental range of the oxidation of analogous compounds (10-20 kcal/mol). The major reaction coordinates of the reaction are the breaking of the O-O bond of H2O2 and the formation of the S-O bond, the transfer of hydrogen to the distal oxygen of hydrogen peroxide occurring after the system has passed the transition state. Reaction barriers of the hydrogen transfer of H2O2 are an average of 10 kcal/mol or higher than the reaction barriers of the oxidation of DMS. Therefore, a two-step oxidation mechanism in which, first, the transfer of a hydrogen atom occurs to form water oxide and, second, the transfer of oxygen to the substrate occurs is unlikely to be correct. Our proposed oxidation mechanism does not suggest a pH dependence of oxidation rate within a moderate range around neutral pH (i.e., under conditions in which hydronium and hydroxide ions do not participate directly in the reaction), and it agrees with experimental observations over moderate pH values. Also, without including a protonated solvent molecule, it has activation energies that correspond to measured activation energies.     

Effects of ion-pairing and hydration on the SNAr reaction of the F- with p-chlorobenzonitrile in aprotic solvents

Theoretical ab initio calculations including liquid phase optimizations were used to investigate the S(N)Ar reaction of the fluoride ion with p-chlorobenzonitrile in dimethyl sulfoxide solution. The effect of the counter ion and hydration of the fluoride ion with one water molecule was analyzed. The calculations indicate that the gas-phase S(N)Ar reaction is more favorable than the corresponding S(N)2 reactions involving fluoride ion and 2-chlorobutane. However, the substantially higher solvent effect on the S(N)Ar reaction makes the nucleophilic substitution on the aromatic ring less favorable than the aliphatic reaction in the liquid phase. For the anhydrous tetrabutylammonium fluoride system, the theoretical free energy barrier of 22.1 kcal mol(-1) is close to the experimental one of 24.4 kcal mol(-1). The smaller tetramethylammonium cation strongly associates with the fluoride ion and increases the barrier by 5 kcal mol(-1). Similarly, just one water molecule hydrating the fluoride ion has the same effect. An analysis of the reaction involving the ion pair and the free anion in different polarity media predicts an unexpected behavior and indicates there is an ideal solvent polarity for each counter ion.     

A study of the hydration of the alkali metal ions in aqueous solution

The hydration of the alkali metal ions in aqueous solution has been studied by large angle X-ray scattering (LAXS) and double difference infrared spectroscopy (DDIR). The structures of the dimethyl sulfoxide solvated alkali metal ions in solution have been determined to support the studies in aqueous solution. The results of the LAXS and DDIR measurements show that the sodium, potassium, rubidium and cesium ions all are weakly hydrated with only a single shell of water molecules. The smaller lithium ion is more strongly hydrated, most probably with a second hydration shell present. The influence of the rubidium and cesium ions on the water structure was found to be very weak, and it was not possible to quantify this effect in a reliable way due to insufficient separation of the O-D stretching bands of partially deuterated water bound to these metal ions and the O-D stretching bands of the bulk water. Aqueous solutions of sodium, potassium and cesium iodide and cesium and lithium hydroxide have been studied by LAXS and M-O bond distances have been determined fairly accurately except for lithium. However, the number of water molecules binding to the alkali metal ions is very difficult to determine from the LAXS measurements as the number of distances and the temperature factor are strongly correlated. A thorough analysis of M-O bond distances in solid alkali metal compounds with ligands binding through oxygen has been made from available structure databases. There is relatively strong correlation between M-O bond distances and coordination numbers also for the alkali metal ions even though the M-O interactions are weak and the number of complexes of potassium, rubidium and cesium with well-defined coordination geometry is very small. The mean M-O bond distance in the hydrated sodium, potassium, rubidium and cesium ions in aqueous solution have been determined to be 2.43(2), 2.81(1), 2.98(1) and 3.07(1) ?, which corresponds to six-, seven-, eight- and eight-coordination. These coordination numbers are supported by the linear relationship of the hydration enthalpies and the M-O bond distances. This correlation indicates that the hydrated lithium ion is four-coordinate in aqueous solution. New ionic radii are proposed for four- and six-coordinate lithium(I), 0.60 and 0.79 ?, respectively, as well as for five- and six-coordinate sodium(I), 1.02 and 1.07 ?, respectively. The ionic radii for six- and seven-coordinate K(+), 1.38 and 1.46 ?, respectively, and eight-coordinate Rb(+) and Cs(+), 1.64 and 1.73 ?, respectively, are confirmed from previous studies. The M-O bond distances in dimethyl sulfoxide solvated sodium, potassium, rubidium and cesium ions in solution are very similar to those observed in aqueous solution.