Thermodynamically dominant hydration structures of aqueous ions

Super-ions of sodium cations with hydrated hydroxide anions: inorganic structure-directing agents in zeolite synthesis

In inorganic zeolite formation, a direct correspondence between liquid state species in the synthesis and the supramolecular decoration of the pores in the as-made final zeolite has never been reported. In this paper, a direct link between the sodium speciation in the synthesis mixture and the pore structure and content of the final zeolite is demonstrated in the example of hydroxysodalite. Super-ions with 4 sodium cations bound by mono- and bihydrated hydroxide are identified as structure-directing agents for the formation of this zeolite. This documentation of inorganic solution species acting as a templating agent in zeolite formation opens new horizons for zeolite synthesis by design.

Thermodynamics of Hydration from the Perspective of the Molecular Quasichemical Theory of Solutions

The quasichemical organization of the potential distribution theorem, molecular quasichemical theory (QCT), enables practical calculations and also provides a conceptual framework for molecular hydration phenomena. QCT can be viewed from multiple perspectives: (a) as a way to regularize an ill-conditioned statistical thermodynamic problem; (b) as an introduction of and emphasis on the neighborship characteristics of a solute of interest; or (c) as a way to include accurate electronic structure descriptions of near-neighbor interactions in defensible statistical thermodynamics by clearly defining neighborship clusters. The theory has been applied to solutes of a wide range of chemical complexity, ranging from ions that interact with water with both long-ranged and chemically intricate short-ranged interactions, to solutes that interact with water solely through traditional van der Waals interations, and including water itself. The solutes range in variety from monatomic ions to chemically heterogeneous macromolecules. A notable feature of QCT is that, in applying the theory to this range of solutes, the theory itself provides guidance on the necessary approximations and simplifications that can facilitate the calculations. In this Perspective, we develop these ideas and document them with examples that reveal the insights that can be extracted using the QCT formulation.

The fluoride permeation pathway and anion recognition in Fluc family fluoride channels

Fluc family fluoride channels protect microbes against ambient environmental fluoride by undermining the cytoplasmic accumulation of this toxic halide. These proteins are structurally idiosyncratic, and thus the permeation pathway and mechanism have no analogy in other known ion channels. Although fluoride-binding sites were identified in previous structural studies, it was not evident how these ions access aqueous solution, and the molecular determinants of anion recognition and selectivity have not been elucidated. Using x-ray crystallography, planar bilayer electrophysiology, and liposome-based assays, we identified additional binding sites along the permeation pathway. We used this information to develop an oriented system for planar lipid bilayer electrophysiology and observed anion block at one of these sites, revealing insights into the mechanism of anion recognition. We propose a permeation mechanism involving alternating occupancy of anion-binding sites that are fully assembled only as the substrate approaches.

The Influence of Spectator Cations on Solvent Reorganization Energy Is a Short-Range Effect

In this manuscript, we use classical molecular dynamics simulation to explore the origin of specific cation effects on the rates of bulk-phase aqueous electron transfer (ET) reactions. We consider 0.6 M solutions of Cl^- and a series of different cations: Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺. We evaluate the collective electrostatic fluctuations that drive Marcus-like ET and find that they are essentially unaffected by changes in the cationic species. This finding implies that the structure making/breaking properties of various cations do not exert a significant influence on bulk-phase ET reactions. We evaluate the role of ion pairing in these specific cation effects and find, unsurprisingly, that model redox anions that are more highly charged tend to pair more effectively with spectator cations than their monovalent counterparts. We demonstrate that this ion pairing significantly affects local electrostatic fluctuations for the anionic redox species and thus conclude that ion pairing is one of the likely sources of rate-dependent cation effects in aqueous ET reactions.

Membrane Exporters of Fluoride Ion

Microorganisms contend with numerous and unusual chemical threats and have evolved a catalog of resistance mechanisms in response. One particularly ancient, pernicious threat is posed by fluoride ion (F^-), a common xenobiotic in natural environments that causes broad-spectrum harm to metabolic pathways. This review focuses on advances in the last ten years toward understanding the microbial response to cytoplasmic accumulation of F^-, with a special emphasis on the structure and mechanisms of the proteins that microbes use to export fluoride: the CLC^F family of F^-/H⁺ antiporters and the Fluc/FEX family of F^- channels.

Quasi-chemical theory of F-(aq): The "no split occupancies rule" revisited

We use ab initio molecular dynamics (AIMD) calculations and quasi-chemical theory (QCT) to study the inner-shell structure of F^-(aq) and to evaluate that single-ion free energy under standard conditions. Following the "no split occupancies" rule, QCT calculations yield a free energy value of -101 kcal/mol under these conditions, in encouraging agreement with tabulated values (-111 kcal/mol). The AIMD calculations served only to guide the definition of an effective inner-shell constraint. QCT naturally includes quantum mechanical effects that can be concerning in more primitive calculations, including electronic polarizability and induction, electron density transfer, electron correlation, molecular/atomic cooperative interactions generally, molecular flexibility, and zero-point motion. No direct assessment of the contribution of dispersion contributions to the internal energies has been attempted here, however. We anticipate that other aqueous halide ions might be treated successfully with QCT, provided that the structure of the underlying statistical mechanical theory is absorbed, i.e., that the "no split occupancies" rule is recognized.

Mini-grand canonical ensemble: Chemical potential in the solvation shell

Quantifying the statistics of occupancy of solvent molecules in the vicinity of solutes is central to our understanding of solvation phenomena. Number fluctuations in small solvation shells around solutes cannot be described within the macroscopic grand canonical framework using a single chemical potential that represents the solvent bath. In this communication, we hypothesize that molecular-sized observation volumes such as solvation shells are best described by coupling the solvation shell with a mixture of particle baths each with its own chemical potential. We confirm our hypotheses by studying the enhanced fluctuations in the occupancy statistics of hard sphere solvent particles around a distinguished hard sphere solute particle. Connections with established theories of solvation are also discussed.

Intramolecular Interactions Overcome Hydration to Drive the Collapse Transition of Gly15

Simulations and experiments show oligo-glycines, polypeptides lacking any side chains, can collapse in water. We assess the hydration thermodynamics of this collapse by calculating the hydration free energy at each of the end points of the reaction coordinate, here taken as the end-to-end distance (r) in the chain. To examine the role of the various conformations for a given r, we study the conditional distribution, P(R_g|r), of the radius of gyration for a given value of r. The free energy change versus R_g, -k_BT ln P(R_g|r), is found to vary more gently compared to the corresponding variation in the excess hydration free energy. Using this observation within a multistate generalization of the potential distribution theorem, we calculate a tight upper bound for the hydration free energy of the peptide for a given r. On this basis, we find that peptide hydration greatly favors the expanded state of the chain, despite primitive hydrophobic effects favoring chain collapse. The net free energy of collapse is seen to be a delicate balance between opposing intrapeptide and hydration effects, with intrapeptide contributions favoring collapse.

Thermodynamics of mixtures of patchy and spherical colloids of different sizes: A multi-body association theory with complete reference fluid information

We present a theory to predict the structure and thermodynamics of mixtures of colloids of different diameters, building on our earlier work [A. Bansal et al., J. Chem. Phys. 145, 074904 (2016)] that considered mixtures with all particles constrained to have the same size. The patchy, solvent particles have short-range directional interactions, while the solute particles have short-range isotropic interactions. The hard-sphere mixture without any association site forms the reference fluid. An important ingredient within the multi-body association theory is the description of clustering of the reference solvent around the reference solute. Here we account for the physical, multi-body clusters of the reference solvent around the reference solute in terms of occupancy statistics in a defined observation volume. These occupancy probabilities are obtained from enhanced sampling simulations, but we also present statistical mechanical models to estimate these probabilities with limited simulation data. Relative to an approach that describes only up to three-body correlations in the reference, incorporating the complete reference information better predicts the bonding state and thermodynamics of the physical solute for a wide range of system conditions. Importantly, analysis of the residual chemical potential of the infinitely dilute solute from molecular simulation and theory shows that whereas the chemical potential is somewhat insensitive to the description of the structure of the reference fluid, the energetic and entropic contributions are not, with the results from the complete reference approach being in better agreement with particle simulations.

The Determination of Absolute Values of Entropies of Hydration [ΔSabs0(H+)h]$[\Delta S_{abs}^0{({H^ + })_h}]$ and Aquation [ΔSabs0(H+)aq]$[\Delta S_{abs}^0{({H^ + })_{aq}}]$ and The Thermodynamics of Proton in Solutions

Absolute entropy value of H+ ion i.e. Δ S aq 0 ( H + ) = −   22.2   J K − 1 mol − 1 $\Delta {\rm{S}}_{{\rm{aq}}}^0({{\rm{H}}^ + }) = - \;22.2{\rm{ }}J{K^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}$ in aqueous solution, a fundamental parameter of importance was determined using a number of extrathermodynamic assumptions of doubtful validity. The value can in no way be regarded to be absolute or correct and needs reassessment. However, no value of the entropy change due to hydration Δ S h 0 ( H + ) $\Delta {\rm{S}}_{\rm{h}}^0({{\rm{H}}^ + })$ was available. Absolute values for entropy of hydration [ Δ S abs 0 ( H + ) h ] $[\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}]$ (entropy change for the transfer of H+ ion from gaseous (g) state to H+ ion in aqueous solution) or entropy of aquation [ Δ S abs 0 ( H + ) aq ] $[\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}]$ (entropy change for transfer of H(g) to aqueous H ion + ) ${\rm{H}}_{{\rm{ion}}}^ + )$ of H+ ion can only be calculated if the related absolute values of Gibbs energy or enthalpy changes of H+ ion i.e. [ Δ G abs 0 ( H + ) h or aq $[\Delta {\rm{G}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\text{h or aq}}}}$ and Δ H abs 0 ( H + ) h or aq ] $\Delta {\rm{H}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\text{h or aq}}}}]$ are known. Critical analysis of the methods used for evaluation of thermodynamics of H+ ion was made. Analysis of the methods showed that the methods had limitations due to defective use of Born equation and ionic additivity principle. Reference electrolyte method using TATB (tetraphenyl arsonium tetraphenyl borate, Ph4AsBPh4), Halliwell and Nyburg’s method and Noyes method or modified Noyes method of Lahiri do not give entropy values. Cluster-ion approximation method (used by Coe and co-workers) gives Δ H abs 0 ( H + ) h $\Delta {\rm{H}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$ and Δ G abs 0 ( H + ) h $\Delta {\rm{G}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$ and hence Δ S abs 0 ( H + ) h = −   153.0  JK − 1 mol − 1 .   Δ S abs 0 ( H + ) aq $\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}} = - \;153.0{\rm{ J}}{{\rm{K}}^{ - 1}}{\rm{mo}}{{\rm{l}}^{ - 1}}.\;\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}$ is obtained by coupling Δ S abs 0 ( H + ) h $\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$ with Δ S abs 0 ( H + ) g $\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{g}}}$ [entropy of gaseous H+ ion calculated using Sackur-Tetrode equation], comes out to be –44.2 JK−1mol−1. However, Δ S abs 0 ( H + ) h $\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{\rm{h}}}$ and Δ S abs 0 ( H + ) aq $\Delta {\rm{S}}_{{\rm{abs}}}^0{({{\rm{H}}^ + })_{{\rm{aq}}}}$ determined by Lahiri and co-workers are –50.0 JK−1mol−1 and 20.0 JK−1mol−1. The values can be regarded to be accurate and reliable. Some comments on the surface potential of water towards Δ G h or aq 0 ( H + ) $\Delta {\rm{G}}_{{\text{h or aq}}}^0({{\rm{H}}^ + })$ and error ranges on the energetics of H+ and other ions are given. No attempt was made to determine entropy of hydration or aquation from theoretical calculations.

Importance of Hydrophilic Hydration and Intramolecular Interactions in the Thermodynamics of Helix-Coil Transition and Helix-Helix Assembly in a Deca-Alanine Peptide

For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state over extended states and the paired helix bundle in the assembly of two helices. The energetic contributions of attractive protein-solvent interactions are separated into quasi-chemical components consisting of a short-range part arising from interactions with solvent in the first hydration shell and the remaining long-range part that is well described by a Gaussian. In the helix-coil transition, short-range attractive protein-solvent interactions outweigh hydrophobic hydration and favor the extended coil states. Analysis of enthalpic effects shows that it is the favorable hydration of the peptide backbone that favors the unfolded state. Protein intramolecular interactions favor the helix state and are decisive in favoring folding. In the pairing of two helices, the cavity contribution outweighs the short-range attractive protein-water interactions. However, long-range, protein-solvent attractive interactions can either enhance or reverse this trend depending on the mutual orientation of the helices. In helix-helix assembly, change in enthalpy arising from change in attractive protein-solvent interactions favors disassembly. In helix pairing as well, favorable protein intramolecular interactions are found to be as important as hydration effects. Overall, hydrophilic protein-solvent interactions and protein intramolecular interactions are found to play a significant role in the thermodynamics of folding and assembly in the system studied.

Encapsulation of [X2(H2O)4]2- (X = F/Cl) clusters by pyridyl terminated tripodal amide receptor in aqueous medium: single crystal X-ray structural evidence

A new tris-amide receptor L based on 1,3,5-methyl substituted benzene platform and pyridyl as an attached unit is synthesized and explored towards anion recognition in aqueous environment. The presence of pyridyl terminal in L facilitates its aqueous solubility. The binding of halides and oxyanions towards L are examined by (1)H-NMR technique in solution and by single crystal X-ray crystallography in solid state studies. Crystallization of fluoride and chloride with L is carried out in acetone-water (1 : 1, v/v) binary solvent mixture that yields crystals for respective host-guest complexes, [L]2·[F2(H2O)4]·[TBA]2 (1) and [L]2·[Cl2(H2O)4]·[TBA]2 (2) suitable for single crystal X-ray diffraction studies. On the other hand, complexation of L with fluoride in dioxane-acetone (1 : 1, v/v) solvent mixture, results the formation of SiF6(2-) encapsulated complex, [L]2·[SiF6(H2O)2]·[TBA]2 (3). Crystallographic result shows the formation of [F2(H2O)4](2-) and [Cl2(H2O)4](2-) zipped 1D-polymeric tweezer-like assemblies of L in acetone-water (1 : 1, v/v) binary solvent mixture in complexes 1 and 2 respectively. Solution state (1)H-NMR studies in D2O-acetone-d6 (1 : 19, v/v) support 1 : 4 (host-guest) binding stoichiometry of F(-), Cl(-), Br(-), NO3(-), HSO4(-) and H2PO4(-) with L. Binding constants of these investigated anions with L by 1 : 1 binding model are calculated which show the following binding order: NO3(-) ≈ HSO4(-) > F(-) ≈ Cl(-) ≈ Br(-) > H2PO4(-). Further, solution state (19)F-NMR studies are also carried out to establish the F(-) binding with L in DMSO-d6.

Inferring Microscopic Kinetic Rates from Stationary State Distributions

We present a principled approach for estimating the matrix of microscopic transition probabilities among states of a Markov process, given only its stationary state population distribution and a single average global kinetic observable. We adapt Maximum Caliber, a variational principle in which the path entropy is maximized over the distribution of all possible trajectories, subject to basic kinetic constraints and some average dynamical observables. We illustrate the method by computing the solvation dynamics of water molecules from molecular dynamics trajectories.

Solvation free energy of the peptide group: its model dependence and implications for the additive-transfer free-energy model of protein stability

The group-additive decomposition of the unfolding free energy of a protein in an osmolyte solution relative to that in water poses a fundamental paradox: whereas the decomposition describes the experimental results rather well, theory suggests that a group-additive decomposition of free energies is, in general, not valid. In a step toward resolving this paradox, here we study the peptide-group transfer free energy. We calculate the vacuum-to-solvent (solvation) free energies of (Gly)n and cyclic diglycine (cGG) and analyze the data according to experimental protocol. The solvation free energies of (Gly)n are linear in n, suggesting group additivity. However, the slope interpreted as the free energy of a peptide unit differs from that for cGG scaled by a factor of half, emphasizing the context dependence of solvation. However, the water-to-osmolyte transfer free energies of the peptide unit are relatively independent of the peptide model, as observed experimentally. To understand these observations, a way to assess the contribution to the solvation free energy of solvent-mediated correlation between distinct groups is developed. We show that linearity of solvation free energy with n is a consequence of uniformity of the correlation contributions, with apparent group-additive behavior in the water-to-osmolyte transfer arising due to their cancellation. Implications for inferring molecular mechanisms of solvent effects on protein stability on the basis of the group-additive transfer model are suggested.

Conditional solvation thermodynamics of isoleucine in model peptides and the limitations of the group-transfer model

The hydration thermodynamics of the amino acid X relative to the reference G (glycine) or the hydration thermodynamics of a small-molecule analog of the side chain of X is often used to model the contribution of X to protein stability and solution thermodynamics. We consider the reasons for successes and limitations of this approach by calculating and comparing the conditional excess free energy, enthalpy, and entropy of hydration of the isoleucine side chain in zwitterionic isoleucine, in extended penta-peptides, and in helical deca-peptides. Butane in gauche conformation serves as a small-molecule analog for the isoleucine side chain. Parsing the hydrophobic and hydrophilic contributions to hydration for the side chain shows that both of these aspects of hydration are context-sensitive. Furthermore, analyzing the solute–solvent interaction contribution to the conditional excess enthalpy of the side chain shows that what is nominally considered a property of the side chain includes entirely nonobvious contributions of the background. The context-sensitivity of hydrophobic and hydrophilic hydration and the conflation of background contributions with energetics attributed to the side chain limit the ability of a single scaling factor, such as the fractional solvent exposure of the group in the protein, to map the component energetic contributions of the model-compound data to their value in the protein. But ignoring the origin of cancellations in the underlying components the group-transfer model may appear to provide a reasonable estimate of the free energy for a given error tolerance.

Anion directed conformational diversities of an arene based hexa-amide receptor and recognition of the [F4(H2O)6]4− cluster

The TOC shows difference in binding energies between different conformers after binding with anions of different dimensionalities and conformers A, B & C show structural diversities with anions in case of L.

Highlights on contemporary recognition and sensing of fluoride anion in solution and in the solid state

The fluoride anion has recently gained well deserved attention among the scientific community for its importance in many fields of human activities, but also for concerns on its effect on health and the environment. Although surprisingly overlooked in systematic studies in the past, fluoride has nowadays become a topical target in the field of anion recognition. A multitude of scientific reports are published every year where the establishment of efficient and specific interaction with fluoride is sought in polar and aqueous media. Here, the emphasis is directed to a detailed description of the most interesting contemporary studies in the field, with a particular focus given to those published in the last few years.

Ion-water clusters, bulk medium effects, and ion hydration

Thermochemistry of gas-phase ion-water clusters together with estimates of the hydration free energy of the clusters and the water ligands are used to calculate the hydration free energy of the ion. Often the hydration calculations use a continuum model of the solvent. The primitive quasichemical approximation to the quasichemical theory provides a transparent framework to anchor such efforts. Here we evaluate the approximations inherent in the primitive quasichemical approach and elucidate the different roles of the bulk medium. We find that the bulk medium can stabilize configurations of the cluster that are usually not observed in the gas phase, while also simultaneously lowering the excess chemical potential of the ion. This effect is more pronounced for soft ions. Since the coordination number that minimizes the excess chemical potential of the ion is identified as the optimal or most probable coordination number, for such soft ions the optimum cluster size and the hydration thermodynamics obtained with and without account of the bulk medium on the ion-water clustering reaction can be different. The ideas presented in this work are expected to be relevant to experimental studies that translate thermochemistry of ion-water clusters to the thermodynamics of the hydrated ion and to evolving theoretical approaches that combine high-level calculations on clusters with coarse-grained models of the medium.

A local entropic signature of specific ion hydration

Monovalent ion hydration entropies are analyzed via energetic partitioning of the potential distribution theorem free energy. Extensive molecular dynamics simulations and free energy calculations are performed over a range of temperatures to determine the electrostatic and van der Waals components of the entropy. The far-field electrostatic contribution is negative and small in magnitude, and it does not vary significantly as a function of ion size, consistent with dielectric models. The local electrostatic contribution, however, varies widely as a function of ion size; the sign yields a direct indication of the kosmotropic (strongly hydrated) or chaotropic (weakly hydrated) nature of the ion hydration. The results provide a thermodynamic signature for specific ion effects in hydration and are consistent with experiments that suggest minimal perturbations of water structure outside the first hydration shell. The hydration entropies are also examined in relation to the corresponding entropies for the isoelectronic rare gas pairs; an inverse correlation is observed, as expected from thermodynamic hydration data.

Communication: Thermodynamics of water modeled using ab initio simulations

We regularize the potential distribution framework to calculate the excess free energy of liquid water simulated with the BLYP-D density functional. Assuming classical statistical mechanical simulations at 350 K model the liquid at 298 K, the calculated free energy is found in fair agreement with experiments, but the excess internal energy and hence also the excess entropy are not. The utility of thermodynamic characterization in understanding the role of high temperatures to mimic nuclear quantum effects and in evaluating ab initio simulations is noted.

Assessing the accuracy of approximate treatments of ion hydration based on primitive quasichemical theory

Quasichemical theory (QCT) provides a framework that can be used to partition the influence of the solvent surrounding an ion into near and distant contributions. Within QCT, the solvation properties of the ion are expressed as a sum of configurational integrals comprising only the ion and a small number of solvent molecules. QCT adopts a particularly simple form if it is assumed that the clusters undergo only small thermal fluctuations around a well-defined energy minimum and are affected exclusively in a mean-field sense by the surrounding bulk solvent. The fluctuations can then be integrated out via a simple vibrational analysis, leading to a closed-form expression for the solvation free energy of the ion. This constitutes the primitive form of quasichemical theory (pQCT), which is an approximate mathematical formulation aimed at reproducing the results from the full many-body configurational averages of statistical mechanics. While the results from pQCT from previous applications are reasonable, the accuracy of the approach has not been fully characterized and its range of validity remains unclear. Here, a direct test of pQCT for a set of ion models is carried out by comparing with the results of free energy simulations with explicit solvent. The influence of the distant surrounding bulk on the cluster comprising the ion and the nearest solvent molecule is treated both with a continuum dielectric approximation and with free energy perturbation molecular dynamics simulations with explicit solvent. The analysis shows that pQCT can provide an accurate framework in the case of a small cation such as Li(+). However, the approximation encounters increasing difficulties when applied to larger cations such as Na(+), and particularly for K(+). This suggests that results from pQCT should be interpreted with caution when comparing ions of different sizes.

Hosting anions. The energetic perspective

Hosting anions addresses the widely spread molecular recognition event of negatively charged species by dedicated organic compounds in condensed phases at equilibrium. The experimentally accessible energetic features comprise the entire system including the solvent, any buffers, background electrolytes or other components introduced for e.g. analysis. The deconvolution of all these interaction types and their dependence on subtle structural variation is required to arrive at a structure-energy correlation that may serve as a guide in receptor construction. The focus on direct host-guest interactions (lock-and-key complementarity) that have dominated the binding concepts of artificial receptors in the past must be widened in order to account for entropic contributions which constitute very significant fractions of the total free energy of interaction. Including entropy necessarily addresses the ambiguity and fuzziness of the host-guest structural ensemble and requires the appreciation of the fact that most liquid phases possess distinct structures of their own. Apparently, it is the perturbation of the intrinsic solvent structure occurring upon association that rules ion binding in polar media where ions are soluble and abundant. Rather than specifying peculiar structural elements useful in anion binding this critical review attempts an illumination of the concepts and individual energetic contributions resulting in the final observation of specific anion recognition (95 references).

Quasichemical and structural analysis of polarizable anion hydration

Quasichemical theory is utilized to analyze the relative roles of solute polarization and size in determining the structure and thermodynamics of bulk anion hydration for the Hofmeister series Cl(-), Br(-), and I(-). Excellent agreement with experiment is obtained for whole salt hydration free energies using the polarizable AMOEBA force field. The total hydration free energies display a stronger dependence on ion size than on polarizability. The quasichemical approach exactly partitions the solvation free energy into inner-shell, outer-shell packing, and outer-shell long-ranged contributions by means of a hard-sphere condition. The inner-shell contribution becomes slightly more favorable with increasing ion polarizability, indicating electrostriction of the nearby waters. Small conditioning radii, even well inside the first maximum of the ion-water(oxygen) radial distribution function, result in Gaussian behavior for the long-ranged contribution that dominates the ion hydration free energy. This in turn allows for a mean-field treatment of the long-ranged contribution, leading to a natural division into first-order electrostatic, induction, and van der Waals terms. The induction piece exhibits the strongest ion polarizability dependence, while the larger-magnitude first-order electrostatic piece yields an opposing but weaker polarizability dependence. The van der Waals piece is small and positive, and it displays a small ion specificity. The sum of the inner-shell, packing, and long-ranged van der Waals contributions exhibits little variation along the anion series for the chosen conditioning radii, targeting electrostatic effects (influenced by ion size) as the largest determinant of specificity. In addition, a structural analysis is performed to examine the solvation anisotropy around the anions. As opposed to the hydration free energies, the solvation anisotropy depends more on ion polarizability than on ion size: increased polarizability leads to increased anisotropy. The water dipole moments near the ion are similar in magnitude to bulk water, while the ion dipole moments are found to be significantly larger than those observed in quantum mechanical studies. Possible impacts of the observed over-polarization of the ions on simulated anion surface segregation are discussed.

Ion selectivity from local configurations of ligands in solutions and ion channels

Probabilities of numbers of ligands proximal to an ion lead to simple, general formulae for the free energy of ion selectivity between different media. That free energy does not depend on the definition of an inner shell for ligand-counting, but other quantities of mechanistic interest do. If analysis is restricted to a specific coordination number, then two distinct probabilities are required to obtain the free energy in addition. The normalizations of those distributions produce partition function formulae for the free energy. Quasi-chemical theory introduces concepts of chemical equilibrium, then seeks the probability that is simplest to estimate, that of the most probable coordination number. Quasi-chemical theory establishes the utility of distributions of ligand-number, and sharpens our understanding of quasi-chemical calculations based on electronic structure methods. This development identifies contributions with clear physical interpretations, and shows that evaluation of those contributions can establish a mechanistic understanding of the selectivity in ion channels.