Hydration of Cl<Superscript>–</Superscript> ion in a planar nanopore with hydrophilic walls. 1. Molecular structure

Computer simulation has been employed to obtain equilibrium molecular configurations, as well as spatial and angular distributions of water molecules, under the action of the field of a single-charged chlorine anion in a model planar nanopore with structureless walls at room temperature. A detailed many-body model of intermolecular interactions calibrated in accordance with experimental data relative to the free energy of hydration in water vapor has been used. The effect of the hydrophilicity of the walls on the ion hydration shell consists in its disintegration into two parts, i.e., molecules retained exclusively due to the interactions with the ion and those adsorbed on the walls. In the regime of strong interactions with the walls, two relatively stable states arise with asymmetric distribution of molecules between opposite walls. The existence of the two metastable states destabilizes the position of ions inside a pore and is expected to accelerate their adsorption on the walls.     

Charge separation in Na<Superscript>+</Superscript>Cl<Superscript>-</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters in water vapors. 2. Free energy

Charge separation in “soft” nanoparticles composed of water molecules, as well as sodium and chlorine ions, is studied by computer simulation. The detailed model of intermolecular interactions that includes, in addition to Coulomb, exchange, and dispersion forces, many-particle polarization and covalent interactions, as well as the effect due to the transfer of excess ion charges and influence of ion field on molecular interactions, is constructed. Model potentials are calibrated using experimental data on the free energy and enthalpy of the addition of vapor molecules to the hydration shells of ions, as well as the data of quantum-chemical calculations for stable cluster configurations and the vibration frequency of interionic bonds. The allowance for many-particle interactions makes it possible to improve the agreement between experimental and quantum-chemical data by more than an order of magnitude. The disregard for many-particle interactions leads to the significant overestimation of cluster stability.     

Charge separation in Na<Superscript>+</Superscript>Cl<Superscript>-</Superscript>(H<Subscript>2</Subscript>O)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript> clusters in water vapors. 1. Intermolecular interactions

Charge separation in “soft” nanoparticles composed of water molecules, as well as sodium and chlorine ions, is studied by computer simulation. The detailed model of intermolecular interactions that includes, in addition to Coulomb, exchange, and dispersion forces, many-particle polarization and covalent interactions, as well as the effect due to the transfer of excess ion charges and influence of ion field on molecular interactions, is constructed. Model potentials are calibrated using experimental data on the free energy and enthalpy of the addition of vapor molecules to the hydration shells of ions, as well as the data of quantum-chemical calculations for stable cluster configurations and the vibration frequency of interionic bonds. The allowance for many-particle interactions makes it possible to improve the agreement between experimental and quantum-chemical data by more than an order of magnitude. The disregard for many-particle interactions leads to the significant overestimation of cluster stability.     

Free energy partitioning analysis of the driving forces that determine ion density profiles near the water liquid-vapor interface

Free energy partitioning analysis is employed to explore the driving forces for ions interacting with the water liquid-vapor interface using recently optimized point charge models for the ions and SPC/E water. The Na(+) and I(-) ions are examined as an example kosmotrope/chaotrope pair. The absolute hydration free energy is partitioned into cavity formation, attractive van der Waals, local electrostatic, and far-field electrostatic contributions. We first compute the bulk hydration free energy of the ions, followed by the free energy to insert the ions at the center of a water slab. Shifts of the ion free energies occur in the slab geometry consistent with the SPC/E surface potential of the water liquid-vapor interface. Then the free energy profiles are examined for ion passage from the slab center to the dividing surface. The profiles show that, for the large chaotropic I(-) ion, the relatively flat total free energy profile results from the near cancellation of several large contributions. The far-field electrostatic part of the free energy, largely due to the water liquid-vapor interface potential, has an important effect on ion distributions near the surface in the classical model. We conclude, however, that the individual forms of the local and far-field electrostatic contributions are expected to be model dependent when comparing classical and quantum results. The substantial attractive cavity free energy contribution for the larger I(-) ion suggests that there is a hydrophobic component important for chaotropic ion interactions with the interface.     

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.     

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.     

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 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.     

Ab initio molecular dynamics study of carbon dioxide and bicarbonate hydration and the nucleophilic attack of hydroxide on CO2

We apply ab initio molecular dynamics (AIMD) to study the hydration structures of the carbon dioxide molecule and the bicarbonate and carbonate anions in liquid water. We also compute the free energy change associated with the nucleophilic attack of the hydroxide ion on carbon dioxide. CO2 behaves like a hydrophobic species and exhibits weak interactions with water molecules. The bicarbonate and carbonate ions are strongly hydrated and coordinate to an average of 6.9 and 8.7 water molecules, respectively. The energetics for the reaction in the gas phase are investigated using density functional theory and second-order M?ller-Plesset perturbation theory (MP2) in conjunction with high-quality basis sets. Using umbrella sampling techniques, we compute the standard state, aqueous phase free energy difference associated with the reaction CO2+OH--->HCO3- after correcting AIMD energies with MP2 results. Our predictions are in good agreement with experiments. The hydration structures along the reaction coordinate, which give rise to a predicted 9.7 kcal/mol standard state free energy barrier, are further analyzed.     

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.     

Hydration of Cl<Superscript>–</Superscript> ion in a planar nanopore with hydrophilic walls. 2. Thermodynamic stability

The Monte Carlo bicanonical statistical ensemble method has been employed to calculate the dependences of the Gibbs free energy, formation work, and entropy on the size of a hydration shell grown from water vapor on single-charged chlorine anion in a model planar nanopore with hydrophilic structureless walls at 298 K. A refined model comprising many-particle polarization interactions and calibrated with respect to experimental data on the free energy and enthalpy of the initial reactions of attachment of water molecules to the ion has been used. It has been found that a weak hydrophilicity of pore walls leads to destabilization of the hydration shell, while a strong one, on the contrary, causes its stabilization. The physical reason for the instability in the field of hydrophilic walls qualitatively differs from that under the conditions of hydration in bulk water vapor.     

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.     

An empirical potential function for the interaction between univalent ions in water

A hydration-shell model has been developed for calculating the interaction energy between ions in water. The hydration shell around each ion contains a few tightly bound water molecules and a larger number of less tightly bound molecules. The energies of their interaction with the ion and the size of the hydration shell have been derived from published experimental data for ion-water clusters in the gas phase. An expression derived for the interaction energy of two univalent ions in water incorporates the following effects: a Lennard-Jones 6–12 interaction, a Coulomb interaction between the charges, the polarization of the hydration shells by a neighboring ion, and an energy term for the removal of water from the hydration shells when the hydration shells of two ions overlap. The effective dielectric constant at small ion-ion distances is the only adjustable parameter. Computed interaction energies for aqueous solutions of twelve alkali halides match experimental values, derived from conductimetric measurements, with an average error of ±14%.     

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.     

Electron capture by a hydrated gaseous peptide: effects of water on fragmentation and molecular survival

The effects of water on electron capture dissociation products, molecular survival, and recombination energy are investigated for diprotonated Lys-Tyr-Lys solvated by between zero and 25 water molecules. For peptide ions with between 12 and 25 water molecules attached, electron capture results in a narrow distribution of product ions corresponding to primarily the loss of 10-12 water molecules from the reduced precursor. From these data, the recombination energy (RE) is determined to be equal to the energy that is lost by evaporating on average 10.7 water molecules, or 4.3 eV. Because water stabilizes ions, this value is a lower limit to the RE of the unsolvated ion, but it indicates that the majority of the available RE is deposited into internal modes of the peptide ion. Plotting the fragment ion abundances for ions formed from precursors with fewer than 11 water molecules as a function of hydration extent results in an energy resolved breakdown curve from which the appearance energies of the b 2 (+), y 2 (+), z 2 (+*), c 2 (+), and (KYK + H) (+) fragment ions formed from this peptide ion can be obtained; these values are 78, 88, 42, 11, and 9 kcal/mol, respectively. The propensity for H atom loss and ammonia loss from the precursor changes dramatically with the extent of hydration, and this change in reactivity can be directly attributed to a "caging" effect by the water molecules. These are the first experimental measurements of the RE and appearance energies of fragment ions due to electron capture dissociation of a multiply charged peptide. This novel ion nanocalorimetry technique can be applied more generally to other exothermic reactions that are not readily accessible to investigation by more conventional thermochemical methods.     

Hydration structure and free energy of biomolecularly specific aqueous dications, including Zn2+ and first transition row metals

The hydration of some of the alkaline earth divalent metal cations and first row transition metal cations is considered within the quasi-chemical theory of solutions. Quantum chemical calculations provide information on the chemically important interactions between the ion and its first-shell water molecules. A dielectric continuum model supplies the outer-shell contribution. The theory then provides the framework to mesh these quantities together. The agreement between the calculated and experimental quantities is good. For the transition metal cations, it is seen that the ligand field contributions play an important role in the physics of hydration. Removing these bonding contributions from the computed hydration free energy results in a linear decrease in the hydration free energy along the period. It is precisely such effects that molecular mechanics force fields have not captured. The implications and extensions of this study to metal atoms in proteins are suggested.     

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.     

Benchmarking the thermodynamic analysis of water molecules around a model beta sheet

Water molecules play a vital role in biological and engineered systems by controlling intermolecular interactions in the aqueous phase. Inhomogeneous fluid solvation theory provides a method to quantify solvent thermodynamics from molecular dynamics or Monte Carlo simulations and provides an insight into intermolecular interactions. In this study, simulations of TIP4P‐2005 and TIP5P‐Ewald water molecules around a model beta sheet are used to investigate the orientational correlations and predicted thermodynamic properties of water molecules at a protein surface. This allows the method to be benchmarked and provides information about the effect of a protein on the thermodynamics of nearby water molecules. The results show that the enthalpy converges with relatively little sampling, but the entropy and thus the free energy require considerably more sampling to converge. The two water models yield a very similar pattern of hydration sites, and these hydration sites have very similar thermodynamic properties, despite notable differences in their orientational preferences. The results also predict that a protein surface affects the free energy of water molecules to a distance of approximately 4.0 Å, which is in line with previous work. In addition, all hydration sites have a favorable free energy with respect to bulk water, but only when the water–water entropy term is included. A new technique for calculating this term is presented and its use is expected to be very important in accurately calculating solvent thermodynamics for quantitative application. © 2012 Wiley Periodicals, Inc.