Ab initio molecular dynamics calculations of ion hydration free energies

Structure and dynamics of the Li+ ion in water, methanol and acetonitrile solvents: ab initio molecular dynamics simulations

Fundamental understanding of the structure and dynamics of the Li+ ion in solution is of utmost importance in different fields of science and technology, especially in the field of ion batteries. In view of this, ab initio molecular dynamics (AIMD) simulations of the LiCl salt in water, methanol and acetonitrile were performed to elucidate structural parameters such as radial distribution function and coordination number, and dynamical properties like diffusion coefficient, limiting ion conductivity and hydrogen bond correlation function. In the present AIMD simulation, one LiCl in water is equivalent to 0.8 M, which is close to the concentration of the lithium salt used in the Li-ion battery. The first sphere of coordination number of the Li+ ion was reaffirmed to be 4. The radial distribution function for different pairs of atoms is seen to be in good agreement with the experimental results. The calculated potential of mean force indicates the stronger interaction of the Li+ ion with methanol over water followed by acetonitrile. The dynamical parameters convey quite high diffusion and limiting ionic conductivity of the Li+ ion in acetonitrile compared to that in water and methanol which has been attributed to the transport of the Li-Cl ion pair in a non-dissociated form in acetonitrile. The AIMD results were found to be in accordance with the experimental findings, i.e. the limiting ion conductivity was found to follow the order acetonitrile > methanol > water. This study shows the importance of atomistic level simulations in evaluating the structural and dynamical parameters and in implementing the results for predicting and synthesizing better next generation solvents for lithium ion batteries (LIBs).

Ion Solvation Free Energy Calculation Based on Ab Initio Molecular Dynamics Using a Hybrid Solvent Model

Free energy calculation of small molecules or ion species in aqueous solvent is one of the most important problems in electrochemistry study. Although there are many previous approaches to calculate such free energies, they are based on ab initio methods and suffer from various limitations and approximations. In the current work, we developed a hybrid approach based on ab initio molecular dynamics (AIMD) simulations to calculate the ion solvation energy. In this approach, a small water cluster surrounding the central ion is used, and implicit solvent model is applied outside the water cluster. A dynamic potential well is used during AIMD to keep the water cluster together. Quasi-harmonic approximation is used to calculate the entropy contribution, while the total energy average is used to calculate the enthalpy term. The obtained solvation voltages of the bulk metal agree with experiments within 0.3 eV, and the simulation results for the solvation energies of gaseous ions are close to the experimental observations. Besides the free energies, radial pair distribution functions and coordination numbers of hydrated cations are also obtained. The remaining challenges of this method are also discussed.

Hydrogen Bond Thermodynamics in Aqueous Acid Solutions: A Combined DFT and Classical Force-Field Approach

The thermodynamics of hydrogen bonds in aqueous and acidic solutions significantly impacts the kinetics and thermodynamics of acid reaction chemistry. We utilize in this work a multiscale approach, combining density functional theory (DFT) with classical molecular dynamics (MD) to model hydrogen bond thermodynamics in an acidic solution. Using thermodynamic cycles, we split the solution phase free energy into its gas phase counterpart plus solvation free energies. We validate this DFT/MD approach by calculating the aqueous phase hydrogen bond free energy between two water molecules (H₂O-···-H₂O), the free energy to transform an H₃O⁺ cation into an H₅O₂⁺ cation, and the hydrogen bond free energy of protonated water clusters (H₃O⁺-···-H₂O and H₅O₂⁺-···-H₂O). The computed equilibrium hydrogen bond free energy of H₂O-···-H₂O is remarkably accurate, especially considering the large individual contributions to the thermodynamic cycle. Turning to cations, we find the ion to be more stable than H₃O⁺ by roughly 1-2 k_BT. This small free energy difference allows for thermal fluctuation between the two idealized motifs, consistent with spectroscopic and simulation studies. Lastly, hydrogen bonding free energies between either H⁺ cation and H₂O in solution were found to be stronger than between two H₂O, though much less so than in vacuum because of dielectric screening in solution. Altogether, our results suggest the DFT/MD approach is promising for application in modeling hydrogen bonding and proton transfer thermodynamics in condensed phases.

Toward a First-Principles Framework for Predicting Collective Properties of Electrolytes

Given the universal importance of electrolyte solutions, it is natural to expect that we have a nearly complete understanding of the fundamental properties of these solutions (e.g., the chemical potential) and that we can therefore explain, predict, and control the phenomena occurring in them. In fact, reality falls short of these expectations. But, recent advances in the simulation and modeling of electrolyte solutions indicate that it should soon be possible to make progress toward these goals. In this Account, we will discuss the use of first-principles interaction potentials based in quantum mechanics (QM) to enhance our understanding of electrolyte solutions. Specifically, we will focus on the use of quantum density functional theory (DFT) combined with molecular dynamics simulation (DFT-MD) as the foundation for our approach. The overarching concept is to understand and accurately reproduce the balance between local or short-ranged (SR) structural details and long-range (LR) correlations, allowing the prediction of the thermodynamics of both single ions in solution as well as the collective interactions characterized by activity/osmotic coefficients. In doing so, relevant collective motions and driving forces characterized by chemical potentials can be determined.In this Account, we will make the case that understanding electrolyte solutions requires a faithful QM representation of the SR nature of the ion-ion, ion-water, and water-water interactions. However, the number of molecules that is required for collective behavior makes the direct application of high-level QM methods that contain the best SR physics untenable, making methods that balance accuracy and efficiency a practical goal. Alternatives such as continuum solvent models (CSMs) and empirically based classical molecular dynamics have been extensively employed to resolve this problem but without yet overcoming the fundamental issue of SR accuracy. We will demonstrate that accurately describing the SR interaction is imperative for predicting both intrinsic properties, namely, at infinite dilution, and collective properties of electrolyte solutions.DFT has played an important role in our understanding of condensed phase systems, e.g., bulk liquid water, the air-water interface, ions in bulk, and at the air-water interface. This approach holds huge promise to provide benchmark calculations of electrolyte solution properties that will allow for the development and improvement of more efficient methods, as well as an enhanced understanding of fundamental phenomena. However, the standard protocol using the generalized gradient approximation with van der Waals (vdW) correction requires improvement in order to achieve a high level of quantitative accuracy. Simply simulating with higher level DFT functionals may not be the best route considering the significant computational cost. Alternative methods of incorporating information from higher levels of QM should be explored; e.g., using force matching techniques on small clusters, where high level benchmark calculations are possible, to develop ideal correction terms to the DFT functional is a promising possibility. We argue that DFT with statistical mechanics is becoming an increasingly useful framework enabling the prediction of collective electrolyte properties.

Computational predictions of metal-macrocycle stability constants require accurate treatments of local solvent and pH effects

Rational design of molecular chelating agents requires a detailed understanding of physicochemical ligand-metal interactions in solvent phase. Computational quantum chemistry methods should be able to provide this, but computational reports have shown poor accuracy when determining absolute binding constants for many chelating molecules. To understand why, we compare and benchmark static- and dynamics-based computational procedures for a range of monovalent and divalent cations binding to a conventional cryptand molecule: 2.2.2-cryptand ([2.2.2]). The benchmarking comparison shows that dynamics simulations using standard OPLS-AA classical potentials can reasonably predict binding constants for monovalent cations, but these procedures fail for divalent cations. We also consider computationally efficient static procedure using Kohn-Sham density functional theory (DFT) and cluster-continuum modeling that accounts for local microsolvation and pH effects. This approach accurately predicts binding energies for monovalent and divalent cations with an average error of 3.2 kcal mol-1 compared to experiment. This static procedure thus should be useful for future molecular screening efforts, and high absolute errors in the literature may be due to inadequate modeling of local solvent and pH effects.

First-principles hydration free energies of oxygenated species at water-platinum interfaces

The hydration free energy of atoms and molecules adsorbed at liquid-solid interfaces strongly influences the stability and reactivity of solid surfaces. However, its evaluation is challenging in both experiments and theories. In this work, a machine learning aided molecular dynamics method is proposed and applied to oxygen atoms and hydroxyl groups adsorbed on Pt(111) and Pt(100) surfaces in water. The proposed method adopts thermodynamic integration with respect to a coupling parameter specifying a path from well-defined non-interacting species to the fully interacting ones. The atomistic interactions are described by a machine-learned inter-atomic potential trained on first-principles data. The free energy calculated by the machine-learned potential is further corrected by using thermodynamic perturbation theory to provide the first-principles free energy. The calculated hydration free energies indicate that only the hydroxyl group adsorbed on the Pt(111) surface attains a hydration stabilization. The observed trend is attributed to differences in the adsorption site and surface morphology.

Ambiguities in solvation free energies from cluster-continuum quasichemical theory: lithium cation in protic and aprotic solvents

Gibbs free energies for Li+ solvation in water, methanol, acetonitrile, DMSO, dimethylacetamide, dimethoxyethane, dimethylformamide, gamma-butyrolactone, pyridine, and sulfolane have been calculated using the cluster-continuum quasichemical theory. With n independent solvent molecules S initial state forming the "monomer" thermodynamic cycle, Li+ solvation free energies are found to be on average 14 kcal mol-1 more positive compared to those from the "cluster" thermodynamic cycle where the initial state is the cluster Sn. We ascribe the inconsistency between the "monomer" and "cluster" cycles mainly to the incorrectly predicted solvation free energies of solvent clusters Sn from the SMD and CPCM continuum solvation models, which is in line with the earlier study of Bryantsev et al., J. Phys. Chem. B, 2008, 112, 9709-9719. When experimental-based solvation free energies of individual solvent molecules and solvent clusters are employed, the "monomer" and "cluster" cycles result in identical numbers. The best overall agreement with experimental-based "bulk" scale lithium cation solvation free energies was obtained for the "monomer" scale, and we recommend this set of values. We expect that further progress in the field is possible if (i) consensus on the accuracy of experimental reference values is achieved; (ii) the most recent continuum solvation models are properly parameterized for all solute-solvent combinations and become widely accessible for testing.

Elusive Coordination of the Ag+ Ion in Aqueous Solution: Evidence for a Linear Structure

X-ray absorption spectroscopy (XAS) has been employed to study the coordination of the Ag⁺ ion in aqueous solution. The conjunction of extended X-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) data analysis provided results suggesting the preference for a first shell linear coordination with a mean Ag-O bond distance of 2.34(2) Å, different from the first generally accepted tetrahedral model with a longer mean Ag-O bond distance. Ab initio molecular dynamics simulations with the Car-Parrinello approach (CPMD) were also performed and were able to describe the coordination of the hydrated Ag⁺ ion in aqueous solution in very good agreement with the experimental data. The high sensitivity for the closest environment of the photoabsorber of the EXAFS and XANES techniques, together with the long-range information provided by CPMD and large-angle X-ray scattering (LAXS), allowed us to reconstruct the three-dimensional model of the coordination geometry around the Ag⁺ ion in aqueous solution. The obtained results from experiments and theoretical simulations provided a complex picture with a certain amount of water molecules with high configurational disorder at distances comprised between the first and second hydration spheres. This evidence may have caused the proliferation of the coordination numbers that have been proposed so far for Ag⁺ in water. Altogether these data show how the description of the hydration of the Ag⁺ ion in aqueous solution can be complex, differently from other metal species where hydration structures can be described by clusters with well-defined geometries. This diffuse hydration shell causes the Ag-O bond distance in the linear [Ag(H₂O)₂]⁺ ion to be ca. 0.2 Å longer than in isolated ions in solid state.

Absolute ion hydration free energy scale and the surface potential of water via quantum simulation

With a goal of determining an absolute free energy scale for ion hydration, quasi-chemical theory and ab initio quantum mechanical simulations are employed to obtain an accurate value for the bulk hydration free energy of the Na⁺ ion. The free energy is partitioned into three parts: 1) the inner-shell or chemical contribution that includes direct interactions of the ion with nearby waters, 2) the packing free energy that is the work to produce a cavity of size λ in water, and 3) the long-range contribution that involves all interactions outside the inner shell. The interfacial potential contribution to the free energy resides in the long-range term. By averaging cation and anion data for that contribution, cumulant terms of all odd orders in the electrostatic potential are removed. The computed total is then the bulk hydration free energy. Comparison with the experimentally derived real hydration free energy produces an effective surface potential of water in the range -0.4 to -0.5 V. The result is consistent with a variety of experiments concerning acid-base chemistry, ion distributions near hydrophobic interfaces, and electric fields near the surface of water droplets.

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.

Reverse Translocation of Nucleotides through a Carbon Nanotube

We report molecular dynamics (MD) simulations of the reverse translocation of single nucleotides through a narrow carbon nanotube (CNT), with a diameter of 1.36 nm, immersed in a 1 M KCl electrolyte solution under an applied electric field along the tube axis. We observe ion selectivity by the narrow CNT, which leads to a high flow of K⁺ ions, in contrast to a negligible and opposing current of Cl^- ions. The K⁺ ions, driven by the electric field, force a negatively charged single nucleotide into the narrow CNT where it is trapped by the incoming K⁺ ions and water molecules, and the nucleotide is driven in the same direction as the K⁺ ions. This illustrates a novel mechanism of nucleotide reverse translocation that is controlled by ion selectivity. An increase in the CNT diameter to 2.71 nm or an increase in nucleotide chain length both lead to translocation in the normal direction of the applied field. The reverse translocation rate of single nucleotides is correlated to the ionic current of K⁺ ions in the narrow tube, unlike translocation in the normal direction in the wider tube.

Sustained release of Ag+ confined inside polyoxometalates for long-lasting bacterial resistance

The release of Ag⁺ confined in the cavities of nanoscale inorganic clusters can be selectively triggered by the Na⁺ present in solutions or biological media for long-lasting bacteriostasis.

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.

Computational Ag/AgCl Reference Electrode from Density Functional Theory-Based Molecular Dynamics

We have developed a scheme to compute the standard potential of the Ag/AgCl reference electrode using density functional theory-based molecular dynamics, similar to the computational standard hydrogen electrode (SHE) developed by Cheng, Sulpizi, and Sprik [J. Chem. Phys. 2009, 131, 154504], with which our new computational reference electrode was compared. We have obtained a similar value of the potential of the Ag/AgCl electrode versus SHE to the experiment. The newly developed computational reference electrode will be extended to nonaqueous solvents in the future, where it will be used to predict standard equilibrium potentials to be compared with experimental data.

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Based on thermodynamic integration, we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas (jellium) as a reference and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this universal choice affords unambiguous and exact definitions of energies and electron densities of AIMs. Numerical results are presented for neutral small molecules (CO, N₂, BF, CO₂), various small molecules with different electronic hybridization states of carbon (CH₄, C₂H₆, C₂H₄, C₂H₂, HCN), and all of the possible BN-doped mutants connecting benzene to borazine (C_2nB_3-nN_3-nH₆, 0 ≤ n ≤ 3). Our results, as well as comparison to atomic energy estimates resulting from either DFT trained neural network models or atomic basis set overlap within CCSD, suggest that APDFT based AIMs enable meaningful, interesting, and counterintuitive interpretations of chemical bonding and molecular electron densities.

"Ion Solvation Spectra": Free Energy Analysis of Solvation Structures of Multivalent Cations in Aprotic Solvents

Using advanced molecular dynamics free energy sampling techniques-both classical and ab initio-we analyze the solvation structures of multivalent cations in aprotic solvents. In contrast to previous studies of mono- and bivalent ions in organic solvents, mainly performed using hybrid cluster-continuum quantum chemistry calculations that rely on the assumption of uniqueness of ion solvation free energies, here we find that monatomic bivalent cations may have multiple well-defined minima, as previously reported only for water, or plateaus of free energy with respect to the ion-solvent coordination. These observations are generalized in the concept of the "ion solvation spectrum" to highlight the rich phenomenology related to ion solvation as opposed to the normally expected free energy profiles with a single coordination minimum. Specifically, we show that a single chemical species may exhibit a multiplicity of distinctly different electrochemical properties. Using one- and two-dimensional projections of the free energy landscape, we analyze the stability of ion solvation structures and reveal minimum free energy pathways for ion (de-)solvation with low-dimensional approximations to associated kinetic barriers. Unexpectedly, we show that in some cases the process of opening the first ion solvation shell, by removing a solvent molecule, may actually drive the ion into a free energy basin with a higher coordination number. Our study highlights some deficiencies of conventional methodologies for studying ion solvation as a path to determine redox potentials and provides experimentally testable predictions.

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.

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.

Computer simulations of alkali-acetate solutions: Accuracy of the forcefields in difference concentrations

When proteins are solvated in electrolyte solutions that contain alkali ions, the ions interact mostly with carboxylates on the protein surface. Correctly accounting for alkali-carboxylate interactions is thus important for realistic simulations of proteins. Acetates are the simplest carboxylates that are amphipathic, and experimental data for alkali acetate solutions are available and can be compared with observables obtained from simulations. We carried out molecular dynamics simulations of alkali acetate solutions using polarizable and non-polarizable forcefields and examined the ion-acetate interactions. In particular, activity coefficients and association constants were studied in a range of concentrations (0.03, 0.1, and 1M). In addition, quantum-mechanics (QM) based energy decomposition analysis was performed in order to estimate the contribution of polarization, electrostatics, dispersion, and QM (non-classical) effects on the cation-acetate and cation-water interactions. Simulations of Li-acetate solutions in general overestimated the binding of Li⁺ and acetates. In lower concentrations, the activity coefficients of alkali-acetate solutions were too high, which is suggested to be due to the simulation protocol and not the forcefields. Energy decomposition analysis suggested that improvement of the forcefield parameters to enable accurate simulations of Li-acetate solutions can be achieved but may require the use of a polarizable forcefield. Importantly, simulations with some ion parameters could not reproduce the correct ion-oxygen distances, which calls for caution in the choice of ion parameters when protein simulations are performed in electrolyte solutions.

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.

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

Alchemical screening of ionic crystals

We introduce alchemical perturbations as a rapid and accurate tool to estimate fundamental structural and energetic properties in pure and mixed ionic crystals.

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

The hydration structure of Ba(2+) ion is important for understanding blocking mechanisms in potassium ion channels. Here, we combine statistical mechanical theory, ab initio molecular dynamics simulations, and electronic structure methods to calculate the hydration free energy and local hydration structure of Ba(2+)(aq). The predicted hydration free energy (-304 ± 1 kcal/mol) agrees with the experimental value (-303 kcal/mol) when a maximally occupied, unimodal inner solvation shell is treated. In the local environment defined by the first shell of hydrating waters, Ba(2+) is directly and stably coordinated by eight (8) waters. Octa-coordination resembles the crystal structure of Ba(2+) and K(+) bound in potassium ion channels, but differs from the local hydration structure of K(+)(aq) determined earlier.

Cluster-continuum quasichemical theory calculation of the lithium ion solvation in water, acetonitrile and dimethyl sulfoxide: an absolute single-ion solvation free energy scale

A solvation free energy scale excluding the net electrostatic potential inside the solute cavity is presented.

The Role of Broken Symmetry in Solvation of a Spherical Cavity in Classical and Quantum Water Models

Insertion of a hard sphere cavity in liquid water breaks translational symmetry and generates an electrostatic potential difference between the region near the cavity and the bulk. Here, we clarify the physical interpretation of this potential and its calculation. We also show that the electrostatic potential in the center of small, medium, and large cavities depends very sensitively on the form of the assumed molecular interactions for different classical simple point-charge models and quantum mechanical DFT-based interaction potentials, as reflected in their description of donor and acceptor hydrogen bonds near the cavity. These differences can significantly affect the magnitude of the scalar electrostatic potential. We argue that the result of these studies will have direct consequences toward our understanding of the thermodynamics of ion solvation through the cavity charging process.

Understanding the rates and molecular mechanism of water-exchange around aqueous ions using molecular simulations

Solvation processes occurring around aqueous ions are of fundamental importance in physics, chemistry, and biology. Over the past few decades, several experimental and theoretical studies were devoted to understanding ion solvation and the processes involved in it. In this article, we present a summary of our recent efforts that, through computer simulations, focused on providing a comprehensive understanding of solvent-exchange processes around aqueous ions. To accomplish these activities, we have looked at the mechanistic properties associated with the water-exchange process, such as potentials of mean force, time-dependent transmission coefficients, and the corresponding rate constants using transition state theory, the reactive flux method, and Grote-Hynes treatments of the dynamic response of the solvent.

An Overview of Electrostatic Free Energy Computations for Solutions and Proteins

Free energy simulations for electrostatic and charging processes in complex molecular systems encounter specific difficulties owing to the long-range, 1/r Coulomb interaction. To calculate the solvation free energy of a simple ion, it is essential to take into account the polarization of nearby solvent but also the electrostatic potential drop across the liquid-gas boundary, however distant. The latter does not exist in a simulation model based on periodic boundary conditions because there is no physical boundary to the system. An important consequence is that the reference value of the electrostatic potential is not an ion in a vacuum. Also, in an infinite system, the electrostatic potential felt by a perturbing charge is conditionally convergent and dependent on the choice of computational conventions. Furthermore, with Ewald lattice summation and tinfoil conducting boundary conditions, the charges experience a spurious shift in the potential that depends on the details of the simulation system such as the volume fraction occupied by the solvent. All these issues can be handled with established computational protocols, as reviewed here and illustrated for several small ions and three solvated proteins.