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.     

Mechanisms for ion retention in molecular water clusters in a planar nanopore against the background of thermal fluctuations

The Monte Carlo method has been used to calculate the potential of mean force for Na⁺ and Cl^? ions interacting in model planar nanopores with structureless walls under the conditions of the material contact with water vapor at room temperature and above water boiling point. The interactions have been described using a detailed many-body model calibrated with respect to experimental data on the free energy of attachment reactions and the results of quantum-chemical calculations. Dissociation becomes possible when the vapor density increases as a sufficient number of molecules are pulled into the field of the ions. The dissociation proceeds sooner under the conditions of the nanopore than in bulk water vapor. Hydration decreases the energy of the dissociated state; however, the entropy component of the free energy partly compensates for the decrease in the internal energy, thereby increasing the stability of a contact ion pair. After the dissociation of a contact ion pair (CIP), ions are retained within a cluster in the state of a solvent-separated ion pair (SSIP). Fluctuations in the number of pulled-in vapor molecules, which are correlated with fluctuations in the interionic distance, stabilize the SSIP states with respect to recombination, while a decrease in the screening of the field of ions under the conditions of the nanopore stabilize the SSIP states with respect to cluster decay. The conditions of the nanopore stimulate the passage of an ion pair from the CIP to the SSIP state due to the rearrangement of the statistical weights in favor of molecules being located in the interionic gap. Thus, under the conditions of the nanopore, the stability of the SSIP states increases with respect to both the recombination of the ions and the decay of the ion-molecular associate.     

Nucleation of water vapor on Na<Superscript>+</Superscript>Cl<Superscript>−</Superscript> ion pairs: Computer simulation

The Monte Carlo method is used to calculate the free energy, entropy, and work of water cluster formation in the field of Na⁺Cl⁻ ion pairs. A detailed model is used that allows for polarization and covalent many-particle interactions, as well as the effects of ion charge reversal. The model is matched to the experimental data on the free energy of ion hydration and the results of the quantum-chemical calculations of stable configurations. The hydration leads to the cleavage of an ion pair in a molecular cluster after approximately ten water molecules are captured. As vapor molecules are added, the stable interion distance monotonically elongates. The low free energy barrier separating the dissociated and nondissociated states of the ion pair in an equilibrium cluster does not hinders the reversible spontaneous transitions between the states, which are responsible for strong fluctuations and the instability of the system. Unlike hydroxonium-containing ion pairs, the formation of long-lived metastable states of hydrated Na⁺Cl⁻ pairs is impossible.     

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.     

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.     

Water vapor clustering in the field of Na<Superscript>+</Superscript> cation inside a nanopore with hydrophilic walls. 1. Spatial organization

Computer simulation has been employed to study the structure of a hydration shell of a Na⁺ ion under the conditions of a planar nanopore with structureless hydrophilic walls at 298 K. Intermolecular interactions have been described in terms of a detailed model calibrated with respect to experimental data on the free energy and enthalpy of the initial reactions of vapor molecule attachment to the ion. In the field of hydrophilic walls, the hydration shell is disrupted into an enveloping part and that spread over the surface of the walls. At the final stage of hydration, states with asymmetric distribution of molecules on opposite walls survive and the phenomenon of ion displacement out of its shell is stably reproduced. The orientational molecular order in the system strongly depends on the degree of wall hydrophilicity. The hydration shell of a sodium ion is less stable with respect to disturbances generated by the field of hydrophilic walls than the shell of a chlorine ion is.     

Structure and electric properties of sodium ion hydrate shell in nanopore with hydrophilic walls

The method of molecular–level computer simulation at the temperature of 298 K was used to study the fundamental regularities of formation of electric properties of the hydrate shell of the Na⁺ cation in a planar model nanopore with hydrophilic structureless walls in contact with water vapors. Electric polarizability changes nonmonotonously: as consistent with the changes in the molecular structure of the system. Hydration within the pore occurs in several stages, from formation of chain structures, microdrop compaction and ejection of the ion from its own hydrate shell to encapsulation and absorption of the ion by the solvent preceding formation of nanoelectrolyte. Despite the significant differences in the energy of retaining hydrate shells for Na⁺ and Cl^─ ions, polarizabilities of the two systems are close and behave similarly under variation of conditions. Strong spatial anisotropy of the polarizability tensor of the ion–hydrate complex is due to the effect of the nanopore walls on multiparticle spatial correlations in the system.     

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.     

Water vapor clustering in the field of a chlorine anion occurring in a planar nanopore with structureless walls

The Monte Carlo bicanonical statistical ensemble method has been employed to calculate the free energy, entropy, and work of Cl^? ion hydration in model planar pores 0.5 and 0.7 nm wide at 298 and 400 K. A detailed model of many-body interactions with the ion has been used, the model being matched to experimental data with respect to the free energy and enthalpy of attachment reaction in water vapor. Under the conditions of a restricted volume, the equilibrium size of a hydration shell substantially decreases, with the effect becoming stronger in the range of moderate and large sizes. In moderately supersaturated vapors, under the conditions of a nanopore, the ion loses its hydration shell as the temperature is decreased. In supersaturated vapors, the hydration shell formed on the ion is thermodynamically stable, while the stability crisis shifts to the region of larger sizes. The enhancement of the thermodynamic stability in the pore results from a rise in the chemical potential of molecules due to the deficiency of closet neighbors and a reduction in the entropy under the conditions of the restricted volume. As the temperature is elevated, the effect of ion displacement out of its hydration shell is leveled. The regularities derived in terms of the estimation model based on the capillary approximation are in qualitative agreement with the results of computer simulation.     

Ion pairs in aqueous electrolyte microdrops under conditions of a flat nanopore

The molecular mechanisms of aqueous solvent penetration into a flat nanopore with hydrophobic structureless walls containing a Na⁺Cl^? ion pair with nonfixed distance between ions is studied by computer simulations. A detailed many-body polycenter model of intermolecular interactions calibrated with respect to experimental data for the free energy of attachment of water vapor molecules and quantum-chemical calculations in clusters is used. The ion pair hydration results in its decomposition. Drawing the molecules into the gap between ions makes easier penetration of solvent and filling of the nanopore with electrolyte. The ion-pair dissociation is accompanied by dramatic changes in the chemical potential of molecules and electric properties of the whole system. The thermodynamic characteristics of decomposition are stable as regards variations in the pore width. The post-decomposition electric polarizability demonstrates strong anisotropy associated with the nanopore flatness.     

The Energy Barrier to Recombination in Hydrated Plasma

An abnormally high potential barrier that separates the H₃O⁺ and Cl^? ions in a cluster of water molecules was revealed. The profile of the barrier was calculated by computer simulation. The calculation was based on a detailed model of intermolecular interactions developed on the basis of experimental data on the free energy and entropy for the addition reactions of water molecules in the vapor phase to the hydration shell of ions in conjunction with the results of quantum-chemical calculations.     

Solvent structures around Na+ and Cl− ions in water

The structural orientation of water in the hydration shells of Na⁺ and Cl^– has been obtained from a Monte Carlo simulation of a 0.55 molal NaCl solution, using the MCY model for water. The probability of first shell coordination numbers has been calculated and is compared with data of previous studies using various model systems.

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Zur Lösungsmittel-Struktur rund um Na⁺ und Cl^– Ionen in Wasser

Zusammenfassung Es wurde mittels einer Monte Carlo-Simulation einer 0.55 molalen NaCl-Lösung unter Verwendung des MCY-Modells für Wasser die Lösungsmittel-orientierung von Wasser in der Hydrat-Hülle von Na⁺ und Cl^–-Ionen erhalten. Die wahrscheinlichsten Koordinationszahlen der ersten Hydrat-Schale werden diskutiert und mit den Daten aus früheren Untersuchungen verschiedener Modellsysteme verglichen.

     

A statistical thermodynamic supermolecule-continuum study of ion hydration: Cell and shell methods

A theoretical study of ion hydration using the statistical thermodynamic supermolecule-continuum method is described. The cell and shell methods are used for configurational averaging. Enthalpies, free energies and entropies are calculated for Li⁺, Na⁺, K⁺, F^– and Cl^– each four coordinated with water. The results are in reasonable accord with experiment. A comparison of the site method, cell method and shell method results is presented. The supermolecule-continuum approach to solvent effects seems to be capable of accommodating essential features for the calculation of solvation energy and solvent effects on structure and properties.     

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.     

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.     

Mean force potential of interaction between Na<Superscript>+</Superscript> and Cl<Superscript>−</Superscript> ions in planar nanopores in contact with water under pressure

The mean force potential (MFP) of interaction between counterions Na⁺ and Cl^? in a planar nanopore with structureless hydrophobic walls is calculated via computer simulation under the condition that the nanopore is in contact with water at an external pressure that exceeds the saturation pressure but remains insufficient to fill the nanopore with water. For a nanopore with a liquid phase, the MFP dependence on the interionic distance indicates the dissociation of an ion pair into two hydrated ions in a nanopore that is not completely filled with water. Fluctuations in the number of water molecules drawn into the interionic space decisively influence the dissociation. The attraction between counterions, averaged over thermal fluctuations, depends largely on the pore width and grows as the shielding of the ions’ electric field by water molecules in a narrow pore diminishes. The contributions from energy and entropy to the free energy of hydration are analyzed.     

Computer simulation of the hydration of a chloride anion in a nanopore with hydrophilic walls

The hydration of a single-charged chloride anion Cl^- in a model plane nanopore with structureless hydrophilic walls in water vapor at room temperature is simulated using the Monte Carlo method. It is established that the adsorption of a fraction of associate molecules Cl^-(H₂O)_N on the walls enhances its thermodynamic stability and simulates the hydration of the ion at low vapor pressures. It is shown that a second stability crisis forms on the curve of the hydration work function in the mode of weak wall hydrophilicity.     

Effect of hydrophilic walls on the hydration of sodium cations in planar nanopores

A computer simulation of the structure of Na⁺ ion hydration shells with sizes in the range of 1 to 100 molecules in a planar model nanopore 0.7 nm wide with structureless hydrophilic walls is performed using the Monte Carlo method at a temperature of 298 K. A detailed model of many-body intermolecular interactions, calibrated with reference to experimental data on the free energy and enthalpy of reactions after gaseous water molecules are added to a hydration shell, is used. It is found that perturbations produced by hydrophilic walls cause the hydration shell to decay into two components that differ in their spatial arrangement and molecular orientational order.     

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.     

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.