Nonpair interactions in Na<Superscript>+</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters under thermal fluctuation conditions

The influence of many-particle interactions on the structure of Na⁺(H₂O) _n clusters at 298 K was studied by the Monte Carlo method. The interaction parameters were reproduced from the experimental data on the Gibbs energy of hydration in water vapor. The interaction of induced dipoles results in the displacement of part of molecules through large distances from the ion. Covalent interactions strengthen the bond with the first attached molecule and weaken bonds with the other molecules.     

Water vapor nucleation on ion pairs under the conditions of a planar nanopore

Computer simulation has been employed to study the effect of a confined space of a planar model pore with structureless hydrophobic walls on the hydration of Na⁺Cl^– ion pairs in water vapor at room temperature. A detailed many-body model of intermolecular interactions has been used. The model has been calibrated relative to experimental data on the free energy and enthalpy of the initial reactions of water molecule attachment to ions and the results of quantum-chemical calculations of the geometry and energy of Na⁺Cl^– (H₂O)_N clusters in stable configurations, as well as spectroscopic data on Na⁺Cl^– dimer vibration frequencies. The free energy and work of hydration, as well as the adsorption curve, have been calculated from the first principles by the bicanonical statistical ensemble method. The dependence of hydration shell size on interionic distance has been calculated by the method of compensation potential. The transition between the states of a contact (CIP) and a solvent-separated ion pair (SSIP) has been reproduced under the conditions of a nanopore. The influence of the pore increases with the hydration shell size and leads to the stabilization of the SSIP states, which are only conditionally stable in bulk water vapor.     

Structural and dynamic investigations of aqueous clusters of Na+ and K+

Using computer modeling, we have studied Na⁺–24H₂O and K⁺–24H₂O clusters. We propose ion-water interaction potentials. We obtain structural, energy, and dynamic characteristics of the studied clusters. We show different mechanisms for exchange of water molecules surrounding the Na⁺ and K⁺ ions: single-particle in the case of Na⁺, and close to K⁺, along with single-particle exchange, a large percentage of multiparticle cooperative exchange of water molecules. This difference is explained by the different degrees of orientation of the water molecules surrounding these ions, by the presence of a unified deformed network of H bonds in the K⁺ cluster and its absence in the Na⁺ cluster. We propose a negative hydration mechanism for the K⁺ ion.Institute of General and Inorganic Chemistry, Russian Academy of Sciences. Institute of Physical Chemistry, Russian Academy of Sciences. Translated from Zhurnal Strukturnoi Khimii, Vol. 34, No. 2, pp. 96–104, March–April, 1993.     

Monte Carlo bicanonical ensemble simulation for sodium cation hydration free energy in liquid water

A series of bicanonical ensemble Monte Carlo (BC MC) simulations has been performed to calculate Na⁺ hydration Gibbs energy in aqueous solution. The hydration Gibbs energy of Na⁺ ion in aqueous solution is the difference between formation free energies of Na⁺ (H₂O)_n and (H₂O)_n clusters at n → α. The convergence of the hydration free energy to bulk water value is fast, and the results at n = 60 turned out to be in good agreement with experimental ones and those calculated using free energy perturbation method [1]. The ion–water interaction has been described by Aqvist's pair potential [1] and SPC model [2] has been used for water–water interactions. The behaviour of the absolute Gibbs energy, the entropy, the internal energy of the clusters and the development of hydration shells’ structure with the increase of the number of water molecules are discussed.     

Theoretical and experimental study of montmorillonite intercalated with tetramethylammonium cation

Structural and vibrational features of Na-montmorillonite and montmorillonite intercalated with tetramethylammonium cation (TMA⁺) were characterized theoretically and experimentally. Theoretical study was performed using density functional theory with inclusion of dispersion corrections. The analysis of the hydrogen bonds in the calculated models has shown that the Na⁺ cations coordinated by six water molecules (Na-M model) are bound to montmorillonite layers by moderate hydrogen bonds between water molecules and basal oxygen atoms of the tetrahedral sheets. Hydrated Na⁺ cations are stabilized by relatively strong hydrogen bonds among water molecules. In the intercalate model, the TMA⁺ cation is fixed in the interlayer space by weak hydrogen bonds between the methyl groups and basal oxygen atoms of montmorillonite layers. The calculated vibrational spectra are in a good agreement with the measured infrared spectra. The detailed analysis of the simulated vibrational spectra allowed unambiguous identification of corresponding bands in the measured spectra and their assignment to the particular vibrational modes. For example, calculations clearly distinguished between AlMgOH and AlAlOH stretching vibrations and also between the coupled vibrations of the methyl groups of the TMA⁺ cations.     

Molecular structure of finely disperse Na+Cl−(H2O) n aerosol particles in water vapor

The thermodynamic states corresponding to solvent separated (SSIP) and contacting (CIP) Na⁺Cl^? ion pairs in molecular water clusters have been obtained by random walks in a configurational space with an equilibrium distribution function at 273 and 150 K. The transition to the SSIP state begins in a thresh-old-type manner in clusters containing 10–12 molecules, with the interionic distance increasing continuously up to disintegration into two hydrated ions with the growth of a hydration shell. As the cluster size increases, the hydration shell shifts from sodium ion to chlorine ion. In the first hydration layer, the electric field of the ions ruptures as many as 50% of hydrogen bonds.     

Reconsideration on Hydration of Sodium Ion: From Micro-Hydration to Bulk Hydration

Micro hydration structures of the sodium ion, [Na(H₂O) _n ]+, n = 1–12, were probed by density functional theory (DFT) at B3LYP/aug-cc-pVDZ level in both gaseous and aqueous phase. The predicted equilibrium sodium–oxygen distance of 0.240 nm at the present level of theory. The four-, five- and six-coordinated cluster can transform from each other at the ambient condition. The analysis of the successive water binding energy and natural charge population (NBO) on Na⁺ clearly shows that the influence of Na⁺ on the surrounding water molecules goes beyond the first hydration shell with the hydration number of 6. The Car-Parrinello molecular dynamic simulation shows that only the first hydration sphere can be found, and the hydration number of Na⁺ is 5.2 and the hydration distance (r_Na–O) is 0.235 nm. All our simulations mentioned in the present paper show an excellent agreement with the diffraction result from X-ray scattering study.     

Study of the structure of molecular complexes. Coordination numbers for Li+, Na+, K+, F− and Cl− in water

A cluster of 200 water molecules containing a single ion (either Li⁺ or Na⁺ or K⁺ or F^? or Cl^?) has been studied at T = 298 K using Monte Carlo techniques. The waterwater interaction is obtained from a quantum-mechanical study of CI type; the ionwater potentials have been obtained from HartreeFock type computations. The computed coordination numbers in the first shell for Li⁺, Na⁺, K⁺, F^? and Cl^? are 4.0, 4.3, 5.1, 3.85 and 4.3, respectively; the corresponding first hydration shell radii are 2.28 Å, 2.59 Å, 3.27 Å, 1.99 Å and 2.85 Å, respectively. A discussion of the second and third hydration shell radii and coordination numbers is given.     

A theoretical study of the hydration of Rb+ by Monte Carlo simulations with refined ab initio-based model potentials

An infinitely diluted aqueous solution of Rb⁺ was studied using ab initio-based model potentials in classical Monte Carlo simulations to describe its structural and thermodynamic features. An existing flexible and polarizable model [Saint-Martin et al. in J Chem Phys 113(24) 10899, 2000] was used for water–water interactions, and the parameters of the Rb⁺–water potential were fitted to reproduce the polarizability of the cation and a sample of ab initio pair interaction energies. It was necessary to calibrate the basis set to be employed as a reference, which resulted in a new determination of the complete basis set (CBS) limit energy of the optimal Rb⁺–OH₂ configuration. Good agreement was found for the values produced by the model with ab initio calculations of three- and four-body nonadditive contributions to the energy, as well as with ab initio and experimental data for the energies, the enthalpies and the geometric parameters of Rb⁺(H₂O) _n clusters, with n = 1,  2,…, 8. Thus validated, the potential was used for simulations of the aqueous solution with three versions of the MCDHO water model; this allowed to assess the relative importance of including flexibility and polarizability in the molecular model. In agreement with experimental data, the Rb⁺–O radial distribution function (RDF) showed three maxima, and hence three hydration shells. The average coordination number was found to be 6.9, with a broad distribution from 4 to 12. The dipole moment of the water molecules in the first hydration shell was tilted to 55° with respect to the ion’s electric field and had a lower value than the average in bulk water; this latter value was recovered at the second shell. The use of the nonpolarizable version of the MCDHO water model resulted in an enhanced alignment to the ion’s electric field, not only in the first, but also in the second hydration shell. The hydration enthalpy was determined from the numerical simulation, taking into account corrections to the interfacial potential and to the spurious effects due to the periodicity imposed by the Ewald sums; the resulting value lied within the range of the various different experimental data. An analysis of the interaction energies between the ion and the water molecules in the different hydration shells and the bulk showed the same partition of the hydration enthalpy as for K⁺. The reason for this similarity is that at distances longer than 3 Å, the ion–water interaction is dominated by the charge-(enhanced) dipole term. Thus, it was concluded that starting at K⁺, the hydration properties of the heavier alkali metal cations should be very similar.     

On the crystallization mechanism of ETS-10 titanosilicate synthesized in gels containing TAABr

Thermal analysis of the products resulted during crystallization of ETS-10 by using starting co gels with molar composition 5.0 Na₂O-3.0 KF-TiO₂-6.4 HCl-TAABr-7.45 SiO₂-197.5 H₂O, where tetralkylammonium (TAA) are tetramethyl (TMA), tetraethyl (TEA), tetrapropyl (TPA) and tetrabutylammonium (TBA), was performed. The effect of TAA⁺ cations (ionic radius in hydrated forms, shapes and hydrophilic/hydrophobic character) on the crystallization of ETS-10 is evident from the induction time, t_i (TMA⁺ ? TEA⁺ < TPA⁺ < TBA⁺), the rate of crystallization, R (TMA⁺ < TEA⁺ < TPA⁺ < TBA⁺), morphology and size of crystallites. Organic cations play a “pore filling” role rather than as a “structure-directing” agent. The relatively flexible molecules of the symmetric tetraalkylammonium cations mixed with alkali cations (Na⁺, K⁺) participate directly at prenucleation and nucleation steps by their interaction with the silicate and titanate in aqueous colloidal dispersion.     

Hydration of the Calcium Dication: Direct Evidence for Second Shell Formation from Infrared Spectroscopy

Infrared laser action spectroscopy in a Fourier‐transform ion cyclotron resonance mass spectrometer is used in conjunction with ab initio calculations to investigate doubly charged, hydrated clusters of calcium formed by electrospray ionization. Six water molecules coordinate directly to the calcium dication, whereas the seventh water molecule is incorporated into a second solvation shell. Spectral features indicate the presence of multiple structures of Ca(H₂O)₇²⁺ in which outer‐shell water molecules accept either one (single acceptor) or two (double acceptor) hydrogen bonds from inner‐shell water molecules. Double‐acceptor water molecules are predominately observed in the second solvent shells of clusters containing eight or nine water molecules. Increased hydration results in spectroscopic signatures consistent with additional second‐shell water molecules, particularly the appearance of inner‐shell water molecules that donate two hydrogen bonds (double donor) to the second solvent shell. This is the first reported use of infrared spectroscopy to investigate shell structure of a hydrated multiply charged cation in the gas phase and illustrates the effectiveness of this method to probe the structures of hydrated ions.     

Revisiting the structure and dynamics of hydrated Cd2+ in aqueous solutions: Insights from the RI-SCS-MP2/MM molecular dynamics simulation

The spin component scale MP2/molecular mechanics molecular dynamics simulation investigated the hydration shell formation and hydrated Cd²⁺ dynamics in the water environment. At the first hydration shell, six water molecules with 2.27 Å for the average distance between water and Cd²⁺. Dynamical properties were analyzed by computing the water molecule's mean residence time (MRT) in its first and second hydration shells. The MRT of each shell was determined to be 31.8 and 1.92 ps, suggesting the strong influence of Cd²⁺ in the first hydration shell. The second shell was labile, with an average number of water molecules being 18. Despite the strong interaction between Cd²⁺ and water molecules in the first shell, the influence of ions in the second hydration shell remained weak.     

Solute�CSolvent Interactions in Aqueous Glycylglycine�CCuCl2 Solutions: Acoustical and Molecular Dynamics Perspective

Acoustical and molecular dynamics studies were carried out to understand the various interactions present in glycylglycine?CCuCl₂ aqueous solutions. Amongst these interactions, hydrogen bonding and solute?Csolvent interactions have been highlighted in this study. The radial distribution function (RDF) was used to investigate solution structure and hydration parameters. Binding of Cu²⁺ with various polar peptide atoms reveals the nature and degree of binding. The formation of complex clusters between glycylglycine and water molecules increases the relaxation time. The first hydration shell considerably influences the structure of the second shell, facilitating the formation of an ordered hydrogen bonded network. Both experimental and theoretical results have proved to be efficient in analyzing the behavior of molecules and to give a clear idea on molecular interactions in solutions.     

Quantum chemical analysis of possible fragmentation of [M + H]<Superscript>+</Superscript> and [M + Na]<Superscript>+</Superscript> complexes of monosubstituted methane,cyclohexane, and benzene derivatives in mass spectrometric studies

The formation and fragmentation energies of the proton and sodium cation complexes with monosubstituted methane, cyclohexane, and benzene derivatives in which carbon atoms are bonded to substituents (NH₂, OH, F, Cl, Br, ONO₂, NO₂, COOH, CN, and Ph) were calculated by the B3LYP/6-31G(d) method. For [M + Na]⁺ complexes, the formation energies are much lower (and differ from one another to a much lesser extent), while the dissociation energies are much higher, than the corresponding energies of the [M + H]⁺ complexes. Na⁺ cation shows a lower selectivity toward localization at functional groups in molecules compared to H⁺. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 246–249, February, 2008.     

Hydration of Fe+: A Monte Carlo simulation of water clusters and of a dilute aqueous solution

Monte Carlo statistical thermodynamic computer simulations are reported for several clusters Fe⁺ (H₂O)_n at different temperatures and for a dilute aqueous solution of Fe⁺ at 298 K. The energy of each configuration has been calculated in the pairwise additivity approximation using the MCY potential for the water–water interaction and an ab initio analytical potential built by us for the Fe⁺–H₂O interaction. Energy and structural analysis of the generated configurations lead to the prediction of a coordination number of six for the first hydration shell of the Fe⁺ ion, both in clusters and in dilute solution. Finally, the variation in the distance to the Fe⁺ ion of the energy and orientation of water molecules in the solution are discussed.     

Structural and Infrared Spectroscopic Study on Solvation of Acetylene by Protonated Water Molecules

The effect of solvation on the conformation of acetylene has been studied by adding one water molecule at a time. Quantum chemical calculations of the H⁺(C₂H₂)(H₂O)_n (n=1-5) clusters indicate that the H₂O molecules prefer to form the OH…π interaction rather than the CH…O interaction. This solvation motif is different from that of neutral (C₂H₂)(H₂O)_n (n=1-4) clusters, in which the H₂O molecules prefer to form the CH…O and OH…C H-bonds. For the H⁺(C₂H₂)(H₂O)_n cationic clusters, the first solvation shell consists of one ring structure with two OH…π H-bonds and three water molecules, which is completed at n=4. Simulated infrared spectra reveal that vibrational frequencies of OH…π H-bonded O-H stretching afford a sensitive probe for exploring the solvation of acetylene by protonated water molecules. Infrared spectra of the H⁺(C₂H₂)(H₂O)_n(n=1-5) clusters could be readily measured by the infrared photodissociation technique and thus provide useful information for the understanding of solvation processes.     

The Structural Features of the Hydrated Ferrous Ion Clusters: [Fe(H2O) n ]2+ (n?=?1–19)

The low-lying structures of the hydrated ferrous ion clusters [Fe(H₂O) _n ]²⁺ (n?=?1?C19) were extensively searched at the level of the density functional theory. The results show that the first hydration shell consists of six water molecules, and the second hydration shell contains seven water molecules. Furthermore, it is found that all the lowest-energy states of [Fe(H₂O) _n ]²⁺ (n?=?1?C19) clusters are spin quintet states. These lowest-energy states keep well even at finite temperatures. The analyses of the successive water binding energy and natural charges population on ferrous ion clearly show that the influence of ferrous ion on the surrounding water molecules goes beyond the second hydration shell.     

Dielectric Properties of Aqueous Solutions of Alkali Metal Sulfates in the Centimeter and Millimeter Bands

The complex permittivity spectra of aqueous solutions of sulfates of Li⁺, Na⁺, K⁺, and Cs⁺ at 298 K were analyzed. It was found that, within the frequency range 7–110 GHz, only one Debye component is observed (which characterizes the total change in the hydration state of water in salt solutions), and there is no separation into hydration shell, transition layer, and bulk water. High-frequency data were used to determine the static permittivities of the solutions over a wide concentration range and the relaxation times, which represent the structural dynamics of water molecules in the studied solutions.     

Structural parameters of glycine zwitterion hydration from the data of the integral equation method in the RISM approach

The structural parameters of glycine zwitterion in water were studied by means of the integral equation method in the framework of the RISM approximation. According to calculations, five water molecules are located in the nearest environment of the -NH ₃ ⁺ group, and two of them are the H-bonded with this group. At the same time, six water molecules are located in the nearest environment of the ?COO^? group, and three of them are the H-bonded with this group. The average number of water molecules in the first hydration shell of ?CH₂ group is four. It has been shown that the probability of hydrogen bond formation between water molecules and the hydrogen atom H1 of the ?NH ₃ ⁺ group is low, and there is no H-bonding between water molecules and the nitrogen atom the ?NH ₃ ⁺ group.     

Hydration of the H<Superscript>+</Superscript>, Li<Superscript>+</Superscript>, Na<Superscript>+</Superscript>, and Cs<Superscript>+</Superscript> ions in MF-4SK perfluorinated sulfonic acid cation-exchange membranes modified with inorganic dopants

The hydration, state, and mobility of protons and Li⁺, Na⁺, and Cs⁺ ions in MF-4SK perfluorinated sulfonic acid cation-exchange membranes doped with silicon dioxide and phosphotungstic acid have been investigated by NMR and impedance spectroscopy. The dopants increase the moisture content of the membrane and change the system of pores and channels in which ion transport takes place. At low humidities, the dopant particles are involved in ion transport. The greatest effect is observed for the membranes doped with both SiO₂ and phosphotungstic acid. The water molecules sorbed by dopant particles as a material participate in the hydration of alkali metal cations in the membrane.