Octa-Coordination and the Aqueous Ba(2+) Ion

Insight into the K channel's selectivity from binding of K+, Na+ and water to N-methylacetamide

In potassium channels that conduct K+ selectively over Na+, which sites are occupied by K+ or water and the mechanism of selectivity are unresolved questions. The combination of the energetics and the constraints imposed by the protein structure yield the selective permeation and occupancy. To gain insight into the combination of structure and energetics, we performed density functional theory (DFT) calculations of multiple N-methyl acetamide (NMA) ligands binding to K+ and Na+, relative to hydrated K+ and Na+. NMA is an analogue of the amino acid backbone and provides the carbonyl binding to the ions that occurs in most binding sites of the K+ channel. Unconstrained optimal structures are obtained through geometry optimization calculations of the NMA ligand binding. The complexes formed by 8 NMA binding to the cations have the O atoms positioned in nearly identical locations as the O atoms in the selectivity filter. The transfer free energies between bulk water and K+ or Na+ bound to 8 NMA are almost identical, implying there is no selectivity by a single site. For water optimized with 8 NMA, binding is weak and O atoms are not positioned as in the K+ channel selectivity filter, suggesting that the ions are much more favored than water. Optimal structures of 8 NMA binding with two cations (K+ or Na+) are stable and have lower binding free energy than the optimal structures with just one cation. However, in the Na+ case, the optimal structure deforms and does not match the K+ channel; that is, two bound Na+ are destabilizing. In contrast, the two K+ structure is stabilized and the selectivity free energy favors K+. Overall, this study shows that binding site occupancy and the mechanism for K+ selectivity involves multiple K+ binding in multiple neighboring layers or sites of the K+ channel selectivity filter.

Binding of carboxylate and water to monovalent cations

The interactions of carboxylate anions with water and cations are important for a wide variety of systems, both biological and synthetic. To gain insight on properties of the local complexes, we apply density functional theory, to treat the complex electrostatic interactions, and investigate mixtures with varied numbers of carboxylate anions (acetate) and waters binding to monovalent cations, Li+, Na+ and K+. The optimal structure with overall lowest free energy contains two acetates and two waters such that the cation is four-fold coordinated, similar to structures found earlier for pure water or pure carboxylate ligands. More generally, the complexes with two acetates have the lowest free energy. In transitioning from the overall optimal state, exchanging an acetate for water has a lower free energy barrier than exchanging water for an acetate. In most cases, the carboxylates are monodentate and in the first solvation shell. As water is added to the system, hydrogen bonding between waters and carboxylate O atoms further stabilizes monodentate structures. These structures, which have strong electrostatic interactions that involve hydrogen bonds of varying strength, are significantly polarized, with ChelpG partial charges that vary substantially as the bonding geometry varies. Overall, these results emphasize the increasing importance of water as a component of binding sites as the number of ligands increases, thus affecting the preferential solvation of specific metal ions and clarifying Hofmeister effects. Finally, structural analysis correlated with free energy analysis supports the idea that binding to more than the preferred number of carboxylates under architectural constraints are a key to ion transport.

Molecular Cage Reports on Its Contents: Spectroscopic Signatures of Cryo-Cooled K+- and Ba2+-Benzocryptand Complexes

UV photofragment spectroscopy and IR-UV double resonance methods are used to determine the structure and spectroscopic responses of a three-dimensional [2.2.2]-benzocryptand cage to the incorporation of a single K⁺ or Ba²⁺ imbedded inside it (labeled as K⁺-BzCrypt, Ba²⁺-BzCrypt). We studied the isolated ion-cryptand complex under cryo-cooled conditions, brought into the gas phase by nano-electrospray ionization. Incorporation of a phenyl ring in place of the central ethyl group in one of the three N-CH₂-CH₂-O-CH₂-CH₂-O-CH₂-CH₂-N chains provides a UV chromophore whose S₀-S₁ transition we probe. K⁺-BzCrypt and Ba²⁺-BzCrypt have their S₀-S₁ origin transitions at 35,925 and 36,446 cm^-1, respectively, blue-shifted by 174 and 695 cm^-1 from that of 1,2-dimethoxybenzene. These origins are used to excite a single conformation of each complex selectively and record their IR spectra using IR-UV dip spectroscopy. The alkyl CH stretch region (2800-3000 cm^-1) is surprisingly sensitive to the presence and nature of the encapsulated ion. We carried out an exhaustive conformational search of cage conformations for K⁺-BzCrypt and Ba²⁺-BzCrypt, identifying two conformations (A and B) that lie below all others in energy. We extend our local mode anharmonic model of the CH stretch region to these strongly bound ion-cage complexes to predict conformation-specific alkyl CH stretch spectra, obtaining quantitative agreement with experiment for conformer A, the gas-phase global minimum. The large electrostatic effect of the charge on the O- and N-lone pairs affects the local mode frequencies of the CH₂ groups adjacent to these atoms. The localized CH₂ scissors modes are pushed up in frequency by the adjacent O/N-atoms so that their overtones have little effect on the alkyl CH stretch region. However, the localized CH₂ wags are nearly degenerate and strongly coupled to one another, producing an array of delocalized wag normal modes, whose highest frequency members reach up above 1400 cm^-1. As such, their overtones mix significantly with the CH stretch modes, most notably involving the CH₂ symmetric stretch fundamentals of the central ethyl groups in the all-alkyl chains and the CH stretches adjacent to the N-atoms and antiperiplanar to the nitrogen lone pair.

Analysis of the First Ion Coordination Sphere: A Toolkit to Analyze the Coordination Sphere of Ions

Rapid and accurate approaches to characterizing the coordination structure of an ion are important for designing ligands and quantifying structure-property trends. Here, we introduce AFICS (Analysis of the First Ion Coordination Sphere), a tool written in Python 3 for analyzing the structural and geometric features of the first coordination sphere of an ion over the course of molecular dynamics simulations. The principal feature of AFICS is its ability to quantify the distortion a coordination geometry undergoes compared to uniform polyhedra. This work applies the toolkit to analyze molecular dynamics simulations of the well-defined coordination structure of aqueous Cr³⁺ along with the more ambiguous structure of aqueous Eu³⁺ chelated to ethylenediaminetetraacetic acid. The tool is targeted for analyzing ions with fluxional or irregular coordination structures (e.g., solution structures of f-block elements) but is generalized such that it may be applied to other systems.

Hydrated Anions: From Clusters to Bulk Solution with Quasi-Chemical Theory

The interactions of hydrated ions with molecular and macromolecular solution and interface partners are strong on a chemical energy scale. Here, we recount the foremost ab initio theory for the evaluation of the hydration free energies of ions, namely, quasi-chemical theory (QCT). We focus on anions, particularly halides but also the hydroxide anion, because they have been outstanding challenges for all theories. For example, this work supports understanding the high selectivity for F^- over Cl^- in fluoride-selective ion channels despite the identical charge and the size similarity of these ions. QCT is built by the identification of inner-shell clusters, separate treatment of those clusters, and then the integration of those results into the broader-scale solution environment. Recent work has focused on a close comparison with mass-spectrometric measurements of ion-hydration equilibria. We delineate how ab initio molecular dynamics (AIMD) calculations on ion-hydration clusters, elementary statistical thermodynamics, and electronic structure calculations on cluster structures sampled from the AIMD calculations obtain just the free energies extracted from the cluster experiments. That theory-experiment comparison has not been attempted before the work discussed here, but the agreement is excellent with moderate computational effort. This agreement reinforces both theory and experiment and provides a numerically accurate inner-shell contribution to QCT. The inner-shell complexes involving heavier halides display strikingly asymmetric hydration clusters. Asymmetric hydration structures can be problematic for the evaluation of the QCT outer-shell contribution with the polarizable continuum model (PCM). Nevertheless, QCT provides a favorable setting for the exploitation of PCM when the inner-shell material shields the ion from the outer solution environment. For the more asymmetrically hydrated, and thus less effectively shielded, heavier halide ions clustered with waters, the PCM is less satisfactory. We therefore investigate an inverse procedure in which the inner-shell structures are sampled from readily available AIMD calculations on the bulk solutions. This inverse procedure is a remarkable improvement; our final results are in close agreement with a standard tabulation of hydration free energies, and the final composite results are independent of the coordination number on the chemical energy scale of relevance, as they should be. Finally, a comparison of anion hydration structure in clusters and bulk solutions from AIMD simulations emphasize some differences: the asymmetries of bulk solution inner-shell structures are moderated compared with clusters but are still present, and inner hydration shells fill to slightly higher average coordination numbers in bulk solution than in clusters.

EXAFS spectroscopy measurements and ab initio molecular dynamics simulations reveal the hydration structure of the radium(II) ion

Radium is refocused from the viewpoint of an environmental pollutant and cancer therapy using alpha particles, where it mainly exists as a hydrated ion. We investigated the radium hydration structure and the dynamics of water molecules by extended X-ray absorption fine structure (EXAFS) spectroscopy and ab initio molecular dynamics (AIMD) simulation. The EXAFS experiment showed that the coordination number and average distance between radium ion and the oxygen atoms in the first hydration shell are 9.2 ± 1.9 and 2.87 ± 0.06 Å, respectively. They are consistent with those obtained from the AIMD simulations, 8.4 and 2.88 Å. The AIMD simulations also revealed that the water molecules in the first hydration shell of radium are less structured and more mobile than those of barium, which is an analogous element of radium. Our results indicate that radium can be more labile than barium in terms of interactions with water.

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Extended X-ray absorption fine structure (EXAFS) measurement revealed the hydration structure of radium ion

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Ab initio molecular dynamics (AIMD) simulation brought consistent results

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AIMD revealed the structural and dynamic properties of the water molecules

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The hydration structure of radium ion is more labile than that of barium ion

Hydration of Heavy Alkaline-Earth Cations Studied by Molecular Dynamics Simulations and X-ray Absorption Spectroscopy

The physicochemical properties of the three heaviest alkaline-earth cations, Sr²⁺, Ba²⁺, and Ra²⁺ in water have been studied by means of classical molecular dynamics (MD) simulations. A specific set of cation-water intermolecular potentials based on ab initio potential energy surfaces has been built on the basis of the hydrated ion concept. The polarizable and flexible model of water MCDHO2 was adopted. The theoretical-experimental comparison of structural, dynamical, energetic, and spectroscopical properties of Sr²⁺ and Ba²⁺ aqueous solutions is satisfactory, which supports the methodology developed. This good behavior allows a reasonable reliability for the predicted Ra²⁺ physicochemical data not experimentally determined yet. Simulated extended X-ray absorption fine-structure (EXAFS) and X-ray absorption near-edge spectroscopy spectra have been computed from the snapshots of the MD simulations and compared with the experimental information available for Sr²⁺ and Ba²⁺. For the Ra²⁺ case, the Ra L₃-edge EXAFS spectrum is proposed. Structural and dynamical properties of the aqua ions for the three cations have been obtained and analyzed. Along the [M(H₂O)_n]^m+ series, the M-O distance for the first-hydration shell is 2.57, 2.81, and 2.93 Å for Sr²⁺, Ba²⁺, and Ra²⁺, respectively. The hydration number also increases when one is going down along the group: 8.1, 9.4, and 9.8 for Sr²⁺, Ba²⁺, and Ra²⁺, respectively. Whereas [Sr(H₂O)₈]²⁺ is a typical aqua ion with a well-defined structure, the Ba²⁺ and Ra²⁺ hydration provides a picture exhibiting an average between the ennea- and the deca-hydration. These results show a similar chemical behavior of Ba²⁺ and Ra²⁺ aqueous solutions and support experimental studies on the removal of Ra-226 of aquifers by different techniques, where Ra²⁺ is replaced by Ba²⁺. A comparison of the heavy alkaline ions, Rb⁺ and Cs⁺, with the heavy alkaline-earth ions is made.

Structural and dynamic properties of some aqueous salt solutions

Aqueous salt solutions are utilized and encountered in wide-ranging technological applications and natural settings. Towards improved understanding of the effect of salts on the dynamic properties of such systems, dilute aqueous salt solutions (up to 1 molar concentration) are investigated here, via experiments and molecular simulations. Four salts are considered: sodium chloride, for which published results are readily available for comparison, ammonium acetate, barium acetate and barium nitrate, for which published data are scarce. In the present work, molecular dynamics (MD) simulations are conducted to quantify viscosity and water self-diffusion coefficients, together with rheometry and Pulsed Field Gradient Spin Echo (PFGSE)-NMR experiments for validation. Simulation predictions are consistent with experimental observations in terms of trend and magnitude of salt-specific effects. Combining insights from the approaches considered, an interpretation of the results is proposed whereby the capacity of salts to influence bulk dynamics arises from their molecular interfacial area and strength of interaction with first hydration-shell water molecules. For the concentration range investigated, the interpretation could be useful in formulating aqueous systems for applications including the manufacturing of advanced catalysts.

Free Energies of Hydrated Halide Anions: High Through-Put Computations on Clusters to Treat Rough Energy-Landscapes

With a longer-term goal of addressing the comparative behavior of the aqueous halides F−, Cl−, Br−, and I− on the basis of quasi-chemical theory (QCT), here we study structures and free energies of hydration clusters for those anions. We confirm that energetically optimal (H2O)nX clusters, with X = Cl−, Br−, and I−, exhibit surface hydration structures. Computed free energies, based on optimized surface hydration structures utilizing a harmonic approximation, typically (but not always) disagree with experimental free energies. To remedy the harmonic approximation, we utilize single-point electronic structure calculations on cluster geometries sampled from an AIMD (ab initio molecular dynamics) simulation stream. This rough-landscape procedure is broadly satisfactory and suggests unfavorable ligand crowding as the physical effect addressed. Nevertheless, this procedure can break down when n≳4, with the characteristic discrepancy resulting from a relaxed definition of clustering in the identification of (H2O)nX clusters, including ramified structures natural in physical cluster theories. With ramified structures, the central equation for the present rough-landscape approach can acquire some inconsistency. Extension of these physical cluster theories in the direction of QCT should remedy that issue, and should be the next step in this research direction.

First-principles modeling of chemistry in mixed solvents: Where to go from here?

Mixed solvents (i.e., binary or higher order mixtures of ionic or nonionic liquids) play crucial roles in chemical syntheses, separations, and electrochemical devices because they can be tuned for specific reactions and applications. Apart from fully explicit solvation treatments that can be difficult to parameterize or computationally expensive, there is currently no well-established first-principles regimen for reliably modeling atomic-scale chemistry in mixed solvent environments. We offer our perspective on how this process could be achieved in the near future as mixed solvent systems become more explored using theoretical and computational chemistry. We first outline what makes mixed solvent systems far more complex compared to single-component solvents. An overview of current and promising techniques for modeling mixed solvent environments is provided. We focus on so-called hybrid solvation treatments such as the conductor-like screening model for real solvents and the reference interaction site model, which are far less computationally demanding than explicit simulations. We also propose that cluster-continuum approaches rooted in physically rigorous quasi-chemical theory provide a robust, yet practical, route for studying chemical processes in mixed solvents.

Hydration Mimicry by Membrane Ion Channels

Ions transiting biomembranes might pass readily from water through ion-specific membrane proteins if these protein channels provide environments similar to the aqueous solution hydration environment. Indeed, bulk aqueous solution is an important reference condition for the ion permeation process. Assessment of this hydration mimicry concept depends on understanding the hydration structure and free energies of metal ions in water in order to provide a comparison for the membrane channel environment. To refine these considerations, we review local hydration structures of ions in bulk water and the molecular quasi-chemical theory that provides hydration free energies. In doing so, we note some current views of ion binding to membrane channels and suggest new physical chemical calculations and experiments that might further clarify the hydration mimicry concept.

Machine Learning-Guided Approach for Studying Solvation Environments

Molecular-level understanding and characterization of solvation environments are often needed across chemistry, biology, and engineering. Toward practical modeling of local solvation effects of any solute in any solvent, we report a static and all-quantum mechanics-based cluster-continuum approach for calculating single-ion solvation free energies. This approach uses a global optimization procedure to identify low-energy molecular clusters with different numbers of explicit solvent molecules and then employs the smooth overlap for atomic positions learning kernel to quantify the similarity between different low-energy solute environments. From these data, we use sketch maps, a nonlinear dimensionality reduction algorithm, to obtain a two-dimensional visual representation of the similarity between solute environments in differently sized microsolvated clusters. After testing this approach on different ions having charges 2+, 1+, 1-, and 2-, we find that the solvation environment around each ion can be seen to usually become more similar in hand with its calculated single-ion solvation free energy. Without needing either dynamics simulations or an a priori knowledge of local solvation structure of the ions, this approach can be used to calculate solvation free energies within 5% of experimental measurements for most cases, and it should be transferable for the study of other systems where dynamics simulations are not easily carried out.

Quasi-Chemical Theory with Cluster Sampling from Ab Initio Molecular Dynamics: Fluoride (F-) Anion Hydration

Accurate predictions of the hydration free energy for anions typically has been more challenging than that for cations. Hydrogen bond donation to the anion in hydrated clusters such as F(H₂O) _n ^- can lead to delicate structures. Consequently, the energy landscape contains many local minima, even for small clusters, and these minima present a challenge for computational optimization. Utilization of cluster experimental results for the free energies of gas-phase clusters shows that even though anharmonic effects are interesting they need not be of troublesome magnitudes for careful applications of quasi-chemical theory to ion hydration. Energy-optimized cluster structures for anions can leave the central ion highly exposed, and application of implicit solvation models to these structures can incur more serious errors than those for metal cations. Utilizing cluster structures sampled from ab initio molecular dynamics simulations substantially fixes those issues.

Strontium and barium in aqueous solution and a potassium channel binding site

Ion hydration structure and free energy establish criteria for understanding selective ion binding in potassium (K⁺) ion channels and may be significant to understanding blocking mechanisms as well. Recently, we investigated the hydration properties of Ba²⁺, the most potent blocker of K⁺ channels among the simple metal ions. Here, we use a similar method of combining ab initio molecular dynamics simulations, statistical mechanical theory, and electronic structure calculations to probe the fundamental hydration properties of Sr²⁺, which does not block bacterial K⁺ channels. The radial distribution of water around Sr²⁺ suggests a stable 8-fold geometry in the local hydration environment, similar to Ba²⁺. While the predicted hydration free energy of -331.8 kcal/mol is comparable with the experimental result of -334 kcal/mol, the value is significantly more favorable than the -305 kcal/mol hydration free energy of Ba²⁺. When placed in the innermost K⁺ channel blocking site, the solvation free energies and lowest energy structures of both Sr²⁺ and Ba²⁺ are nearly unchanged compared with their respective hydration properties. This result suggests that the block is not attributable to ion trapping due to +2 charge, and differences in blocking behavior arise due to free energies associated with the exchange of water ligands for channel ligands instead of free energies of transfer from water to the binding site.

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.

Assessment of Simple Models for Molecular Simulation of Ethylene Carbonate and Propylene Carbonate as Solvents for Electrolyte Solutions

Progress in understanding liquid ethylene carbonate (EC) and propylene carbonate (PC) on the basis of molecular simulation, emphasizing simple models of interatomic forces, is reviewed. Results on the bulk liquids are examined from the perspective of anticipated applications to materials for electrical energy storage devices. Preliminary results on electrochemical double-layer capacitors based on carbon nanotube forests and on model solid-electrolyte interphase (SEI) layers of lithium ion batteries are considered as examples. The basic results discussed suggest that an empirically parameterized, non-polarizable force field can reproduce experimental structural, thermodynamic, and dielectric properties of EC and PC liquids with acceptable accuracy. More sophisticated force fields might include molecular polarizability and Buckingham-model description of inter-atomic overlap repulsions as extensions to Lennard-Jones models of van der Waals interactions. Simple approaches should be similarly successful also for applications to organic molecular ions in EC/PC solutions, but the important case of Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ deserves special attention because of the particularly strong interactions of that small ion with neighboring solvent molecules. To treat the Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ ions in liquid EC/PC solutions, we identify interaction models defined by empirically scaled partial charges for ion-solvent interactions. The empirical adjustments use more basic inputs, electronic structure calculations and ab initio molecular dynamics simulations, and also experimental results on Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ thermodynamics and transport in EC/PC solutions. Application of such models to the mechanism of Li\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^+$$\end{document}+ transport in glassy SEI models emphasizes the advantage of long time-scale molecular dynamics studies of these non-equilibrium materials.

Divalent ions are potential permeating blockers of the non-selective NaK ion channel: combined QM and MD based investigations

The interplay between the hydration energy barrier and optimum site-selectivity controls the permeation and blocking features of divalent metal ions.

Ion-Specific Effects in Carboxylate Binding Sites

Specific ion binding by carboxylates (-COO^-) is a broadly important topic because -COO^- is one of the most common functional groups coordinated to metal ions in metalloproteins and synthetic polymers. We apply quantum chemical methods and the quasi-chemical free-energy theory to investigate how variations in the number of -COO^- ligands in a binding site determine ion-binding preferences. We study a series of monovalent (Li⁺, Na⁺, K⁺, Cs⁺) and divalent (Zn²⁺, Ca²⁺) ions relevant to experimental work on ion channels and ionomers. Of two competing hypotheses, our results support the ligand field strength hypothesis and follow the reverse Hofmeister series for ion solvation and ion transfer from aqueous solution to binding sites with the preferred number of ligands. New insight arises from the finding that ion-binding sequences can be manipulated and even reversed just by constraining the number of carboxylate ligands in the binding sites. Our results help clarify the discrepancy in ion association between molecular ligands in aqueous solutions and ionomers, and their chemical analogues in ion-channel binding sites.