The thermodynamics of proton hydration and the electrochemical surface potential of water

NMR Spectroscopy and Multiscale Modeling Shed Light on Ion-Solvent Interactions and Ion Pairing in Aqueous NaF Solutions

The balance between ion solvation and ion pairing in aqueous solutions modulates chemical and physical processes from catalysis to protein folding. Yet, despite more than a century of investigation, experimental determination of the distribution of ion-solvation and ion-pairing states remains elusive, even for archetypal systems like aqueous alkali halides. Here, we combine nuclear magnetic resonance (NMR) spectroscopy and multiscale modeling to disentangle ion-solvent interactions from ion pairing in aqueous sodium fluoride solutions. We have developed a high-accuracy method to collect experimental NMR resonance frequencies for both ions as functions of temperature and concentration. Comparison of these data with resonance frequencies for nonassociating salts allows us to differentiate the influence of solvation and ion pairing on NMR spectra. These high-quality experimental NMR data are used to validate our modeling framework comprising polarizable force field molecular dynamics (MD) simulations and quantum chemical calculations of NMR resonance frequencies. Our experimental and theoretical resonance frequency shifts agree over a wide range of temperatures and concentrations. Structural analysis reveals how both trends are dominated by interactions with water molecules. For the more sensitive 19F nucleus, the NMR resonance frequency decreases as hydrogen bonds between fluoride and water molecules are reduced in number with increased temperature and molality. Through a detailed analysis of the theoretical NMR resonance frequencies for both ions, we show that NMR spectroscopy can distinguish both contact ion pairs and single-solvent-separated ion pairs from free ions. This quantitative framework can be applied directly to other systems.

The real reason why ATP hydrolysis is spontaneous at pH > 7: It's (mostly) the proton concentration!

Common wisdom holds that ATP hydrolysis is spontaneous because of the weakness of its phosphoanhydride bonds, electrostatic repulsion within the polyanionic ATP4- molecule, and resonance stabilization of the inorganic phosphate and ADP products. By examining the pH-dependence of the hydrolysis Gibbs free energy, we show that in fact, above pH 7, ATP hydrolysis is spontaneous due mainly to the low concentration of the H+ that is released as product. Hence, ATP is essentially just an electrophilic target whose attack by H2 O causes the acidity of the water nucleophile to increase dramatically; the spontaneity of the resulting acid ionization supplies much of the released Gibbs free energy. We also find that fermentation lowers pH not due to its organic acid products (e.g., lactic, acetic, formic, or succinic acids), but again, due to the H+ product of ATP hydrolysis.

Measurements and Utilization of Consistent Gibbs Energies of Transfer of Single Ions: Towards a Unified Redox Potential Scale for All Solvents

Utilizing the "ideal" ionic liquid salt bridge to measure Gibbs energies of transfer of silver ions between the solvents water, acetonitrile, propylene carbonate and dimethylformamide results in a consistent data set with a precision of 0.6 kJ mol-1 over 87 measurements in 10 half-cells. This forms the basis for a coherent experimental thermodynamic framework of ion solvation chemistry. In addition, we define the solvent independent pe abs H 2 O - and the E abs H 2 O values that account for the electronating potential of any redox system similar to the pH abs H 2 O value of a medium that accounts for its protonating potential. This E abs H 2 O scale is thermodynamically well-defined enabling a straightforward comparison of the redox potentials (reducities) of all media with respect to the aqueous redox potential scale, hence unifying all conventional solvents' redox potential scales. Thus, using the Gibbs energy of transfer of the silver ion published herein, one can convert and unify all hitherto published redox potentials measured, for example, against ferrocene, to the E abs H 2 O scale.

Impacts of targeting different hydration free energy references on the development of ion potentials

Hydration free energy (HFE) as the most important solvation parameter is often targeted in ion model development, even though the reported values differ by dozens of kcal mol^-1 mainly due to the experimentally undetermined HFE of the proton ΔG°(H⁺). The choice of ΔG°(H⁺) obviously affects the hydration of single ions and the relative HFE between the ions with different (magnitude or sign) charges, and the impacts of targeted HFEs on the ion solvation and ion-ion interactions are largely unrevealed. Here we designed point charge models of K⁺, Mg²⁺, Al³⁺, and Cl^- ions targeting a variety of HFE references and then investigated the HFE influences on the simulations of dilute and concentrated ion solutions and of the salt ion pairs in gas, liquid, and solid phases. Targeting one more property of ion-water oxygen distances (IOD) leaves the ion-water binding distance invariant, while the binding strength increases with the decreasing (more negative) HFE of ions as a result of a decrease in ΔG°(H⁺) for the cation and an increase in ΔG°(H⁺) for the anion. The increase in ΔG°(H⁺) leads to strengthened cation-anion interactions and thus to close ion-ion contacts, low osmotic pressures, and small activity derivatives in concentrated ion solutions as well as too stable ion pairs of the salts in different phases. The ion diffusivity and water exchange rates around the ions are simply not HFE dependent but rather more complex. Targeting both the aqueous IOD and salt crystal properties of KCl was also attempted and the comparison between different models indicates the complexity and challenge in obtaining a balanced performance between different phases using classical force fields. Our results also support that a real ΔG°(H⁺) value of -259.8 kcal mol^-1 recommended by Hünenberger and Reif guides ion models to reproduce ion-water and ion-ion interactions reasonably at relatively low salt concentrations. Simulations of a metalloprotein show that a relatively more positive ΔG°(H⁺) for Mg²⁺ model is better for a reasonable description of the metal binding network.

Condensed Phase Water Molecular Multipole Moments from Deep Neural Network Models Trained on Ab Initio Simulation Data

Ionic solvation phenomena in liquids involve intense interactions in the inner solvation shell. For interactions beyond the first shell, the ion-solvent interaction energies result from the sum of many smaller-magnitude contributions that can still include polarization effects. Deep neural network (DNN) methods have recently found wide application in developing efficient molecular models that maintain near-quantum accuracy. Here we extend the DeePMD-kit code to produce accurate molecular multipole moments in the bulk and near interfaces. The new method is validated by comparing the DNN moments with those generated by ab initio simulations. The moments are used to compute the electrostatic potential at the center of a molecular-sized hydrophobic cavity in water. The results show that the fields produced by the DNN models are in quantitative agreement with the AIMD-derived values. These efficient methods will open the door to more accurate solvation models for large solutes such as proteins.

Developing and Assessing Nonbonded Dummy Models of Magnesium Ion with Different Hydration Free Energy References

A large diversity in the targeted hydration free energies (HFEs) during model parameterization of metal ions was reported in the literature with a difference by dozens of kcal/mol. Here, we developed a series of nonbonded dummy models of the Mg²⁺ ion targeting different HFE references in TIP3P water, followed by assessments of the designed models in the simulations of MgCl₂ solution and biological systems. Together with the comparison of existing models, we conclude that the difference in the targeted HFEs has a limited influence on the model performance, while the usability of these models differs from case to case. The feasibility of reproducing more properties of Mg²⁺ such as diffusion constants and water exchange rates using a nonbonded dummy model is demonstrated. Underestimated activity derivative and osmotic coefficient of MgCl₂ solutions in high concentration reveal a necessity for further optimization of ion-pair interactions. The developed dummy models are applicable to metal coordination with Asp, Glu, and His residues in metalloenzymes, and the performance in predicting monodentate or bidentate binding modes of Asp/Glu residues depends on the complexity of metal centers and the choice of protein force fields. When both the binding modes coexist, the nonbonded dummy models outperform point charge models, probably in need of considering polarization of metal-binding residues by, for instance, charge calibration in classical force fields. This work is valuable for the use and further development of magnesium ion models for simulations of metal-containing systems with good accuracy.

Uncovering Differences in Hydration Free Energies and Structures for Model Compound Mimics of Charged Side Chains of Amino Acids

Free energies of hydration are of fundamental interest for modeling and understanding conformational and phase equilibria of macromolecular solutes in aqueous phases. Of particular relevance to systems such as intrinsically disordered proteins are the free energies of hydration and hydration structures of model compounds that mimic charged side chains of Arg, Lys, Asp, and Glu. Here, we deploy a Thermodynamic Cycle-based Proton Dissociation (TCPD) approach in conjunction with data from direct measurements to obtain estimates for the free energies of hydration for model compounds that mimic the side chains of Arg+, Lys+, Asp-, and Glu-. Irrespective of the choice made for the hydration free energy of the proton, the TCPD approach reveals clear trends regarding the free energies of hydration for Arg+, Lys+, Asp-, and Glu-. These trends include asymmetries between the hydration free energies of acidic (Asp- and Glu-) and basic (Arg+ and Lys+) residues. Further, the TCPD analysis, which relies on a combination of experimental data, shows that the free energy of hydration of Arg+ is less favorable than that of Lys+. We sought a physical explanation for the TCPD-derived trends in free energies of hydration. To this end, we performed temperature-dependent calculations of free energies of hydration and analyzed hydration structures from simulations that use the polarizable Atomic Multipole Optimized Energetics for Biomolecular Applications (AMOEBA) force field and water model. At 298 K, the AMOEBA model generates estimates of free energies of hydration that are consistent with TCPD values with a free energy of hydration for the proton of ca. -259 kcal/mol. Analysis of temperature-dependent simulations leads to a structural explanation for the observed differences in free energies of hydration of ionizable residues and reveals that the heat capacity of hydration is positive for Arg+ and Lys+ and negative for Asp- and Glu-.

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.

Transferable interactions of Li+ and Mg2+ ions in polarizable models

Therapeutic implications of Li⁺, in many cases, stem from its ability to inhibit certain Mg²⁺-dependent enzymes, where it interacts with or substitutes for Mg²⁺. The underlying details of its action are, however, unknown. Molecular simulations can provide insights, but their reliability depends on how well they describe relative interactions of Li⁺ and Mg²⁺ with water and other biochemical groups. Here, we explore, benchmark, and recommend improvements to two simulation approaches: the one that employs an all-atom polarizable molecular mechanics (MM) model and the other that uses a hybrid quantum and MM implementation of the quasi-chemical theory (QCT). The strength of the former is that it describes thermal motions explicitly and that of the latter is that it derives local contributions from electron densities. Reference data are taken from the experiment, and also obtained systematically from CCSD(T) theory, followed by a benchmarked vdW-inclusive density functional theory. We find that the QCT model predicts relative hydration energies and structures in agreement with the experiment and without the need for additional parameterization. This implies that accurate descriptions of local interactions are essential. Consistent with this observation, recalibration of local interactions in the MM model, which reduces errors from 10.0 kcal/mol to 1.4 kcal/mol, also fixes aqueous phase properties. Finally, we show that ion-ligand transferability errors in the MM model can be reduced significantly from 10.3 kcal/mol to 1.2 kcal/mol by correcting the ligand's polarization term and by introducing Lennard-Jones cross-terms. In general, this work sets up systematic approaches to evaluate and improve molecular models of ions binding to proteins.

Unexpected Properties of Degassed Solutions

Theories of liquids and their simulation ignore any physical effects of dissolved atmospheric gas. Solubilities appear far too low to matter. Long-standing observations to the contrary, like cavitation, the salt dependence of bubble-bubble interactions, and the stability of degassed emulsions, continue to call that assumption into question, and these questions multiply. We herein explore more unexpected effects of dissolved gas that are inexplicable by classical theory. Electrical conductivities of different salts in water were measured as a function of concentration before and after degassing the liquid. The liquid/liquid phase separation of binary mixtures containing water, n-hexane, or perfluorooctane was significantly retarded after degassing. We anticipate that preliminary attempts at explaining these effect probably lie in self-organization of dissolved gas, like nanobubbles and cooperativity in gas molecular interactions. These are salt- and liquid-dependent.

Prediction of Solvation Free Energies of Ionic Solutes in Neutral Solvents

The prediction of solvation free energies is essential for a variety of applications. Solvation free energies of neutral systems can be predicted quite accurately. The accuracy of predictions for solvation free energies of ionic solutes dissolved in neutral solvents, however, has been reported to be worse by at least 1 order of magnitude. In this study, the performance of three approaches for solvation free energy prediction of several hundred ions dissolved in neutral solvents is evaluated. The applied methods are COSMO-RS, cluster continuum model (CCM) together with COSMO-RS, and COSMO-RS-ES. It is emphasized that the reference data for model evaluation are subject to large uncertainties stemming from the impossibility to measure the so-called elusive absolute free energies of solvation of a single ion. Consequently, such uncertainty must be considered during the evaluation of prediction methods. Therefore, a straightforward approach to account for the underlying uncertainty is applied here. Hereby, it is revealed that the true performance of the method is better than what is often reported. The average absolute deviation (AAD) of COSMO-RS is calculated to be 2.3 kcal mol^-1, while applying the CCM and COSMO-RS-ES each results in AADs of 2.0 kcal mol^-1. This accuracy allows for qualitative assessment of solvation free energy-dependent quantities, such as reaction rate constants.

Large-Sized Ammonia Clusters and Solvation Energies of the Proton in Ammonia

The absolute solvation energies (free energies and enthalpies) of the proton in ammonia are used to compute the pK_a of species embedded in ammonia. They are also used to compute the solvation energies of other ions in ammonia. Despite their importance, it is not possible to determine experimentally the solvation energies of the proton in a given solvent. We propose in this work a direct approach to compute the solvation energies of the proton in ammonia from large-sized neutral and protonated ammonia clusters. To undertake this investigation, we performed a geometry optimization of neutral and protonated ammonia 30-mer, 40-mer, and 50 mer to locate stable structures. These structures have been fully optimized at both APFD/6-31++g(d,p) and M06-2X/6-31++g(d,p) levels of theory. An infrared spectroscopic study of these structures has been provided to assess the reliability of our investigation. Using these structures, we have computed the absolute solvation free energy and the absolute solvation enthalpy of the proton in ammonia. It comes out that the absolute solvation free energy of the proton in ammonia is calculated to be -1192 kJ mol^-1 , whereas the absolute solvation enthalpy is evaluated to be -1214 kJ mol^-1 . © 2019 Wiley Periodicals, Inc.

Fast and accurate calculation of hydration energies of molecules and ions

An accurate and efficient method for calculation of hydration free energy of ions and neutral molecules is presented.

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.

Ion hydration free energies and water surface potential in water nano drops: The cluster pair approximation and the proton hydration Gibbs free energy in solution

We estimate both single ion hydration Gibbs free energies in water droplets, comprising from 50 to 1000 molecules, and water/vacuum surface potentials in pure water droplets comprising up to 10 000 molecules. We consider four ions, namely, Li⁺, NH₄ ⁺, F^-, and Cl^-, and we model their hydration process and water/water interactions using polarizable force fields based on an induced point dipole approach. We show both ion hydration Gibbs free energies and water surface potentials to obey linear functions of the droplet radius as soon as droplets comprising a few hundred water molecules. Moreover, we also show that the differences in anion/cation hydration Gibbs free energies in droplets obey a different regime in large droplets than in small clusters comprising no more than six water molecules, in line with the earlier results computed from standard additive point charge force fields. Hence, both point charge and more sophisticated induced point dipole molecular modeling approaches suggest that methods considering only the thermodynamical properties of small ion/water clusters to estimate the absolute proton hydration Gibbs free energy in solution are questionable. In particular, taking into account the data of large ion/water droplets may yield a proton hydration Gibbs free energy in solution value to be shifted by several k_BT units compared to small clusters-based approaches.

Reaction of Electrons with DNA: Radiation Damage to Radiosensitization

This review article provides a concise overview of electron involvement in DNA radiation damage. The review begins with the various states of radiation-produced electrons: Secondary electrons (SE), low energy electrons (LEE), electrons at near zero kinetic energy in water (quasi-free electrons, (e-qf)) electrons in the process of solvation in water (presolvated electrons, e-pre), and fully solvated electrons (e-aq). A current summary of the structure of e-aq, and its reactions with DNA-model systems is presented. Theoretical works on reduction potentials of DNA-bases were found to be in agreement with experiments. This review points out the proposed role of LEE-induced frank DNA-strand breaks in ion-beam irradiated DNA. The final section presents radiation-produced electron-mediated site-specific formation of oxidative neutral aminyl radicals from azidonucleosides and the evidence of radiosensitization provided by these aminyl radicals in azidonucleoside-incorporated breast cancer cells.

Single-Ion Thermodynamics from First Principles: Calculation of the Absolute Hydration Free Energy and Single-Electrode Potential of Aqueous Li+ Using ab Initio Quantum Mechanical/Molecular Mechanical Molecular Dynamics Simulations

A recently proposed thermodynamic integration (TI) approach formulated in the framework of quantum mechanical/molecular mechanical molecular dynamics (QM/MM MD) simulations is applied to study the structure, dynamics, and absolute intrinsic hydration free energy Δ_s G_M⁺,wat^◦ of the Li⁺ ion at a correlated ab initio level of theory. Based on the results, standard values (298.15 K, ideal gas at 1 bar, ideal solute at 1 molal) for the absolute intrinsic hydration free energy [Formula: see text] of the proton, the surface electric potential jump χ_wat^◦ upon entering bulk water, and the absolute single-electrode potential [Formula: see text] of the reference hydrogen electrode are calculated to be -1099.9 ± 4.2 kJ·mol^-1, 0.13 ± 0.08 V, and 4.28 ± 0.04 V, respectively, in excellent agreement with the standard values recommended by Hünenberger and Reif on the basis of an extensive evaluation of the available experimental data (-1100 ± 5 kJ·mol^-1, 0.13 ± 0.10 V, and 4.28 ± 0.13 V). The simulation results for Li⁺ are also compared to those for Na⁺ and K⁺ from a previous study in terms of relative hydration free energies ΔΔ_s G_M⁺,wat^◦ and relative electrode potentials [Formula: see text]. The calculated values are found to agree extremely well with the experimental differences in standard conventional hydration free energies ΔΔ_s G_M⁺,wat^• and redox potentials [Formula: see text]. The level of agreement between simulation and experiment, which is quantitative within error bars, underlines the substantial accuracy improvement achieved by applying a highly demanding QM/MM approach at the resolution-of-identity second-order Møller-Plesset perturbation (RIMP2) level over calculations relying on purely molecular mechanical or density functional theory (DFT) descriptions. A detailed analysis of the structural and dynamical properties of the Li⁺ hydrate indicates that a correct description of the solvation structure and dynamics is achieved as well at this level of theory. Consideration of the QM/MM potential-energy components also shows that the partitioning into QM and MM zones does not induce any significant energetic artifact for the system considered.

Solvation energies of the proton in methanol revisited and temperature effects

Various functionals assessing solvation free energies and enthalpies of the proton in methanol.

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.

Origin of Asymmetric Solvation Effects for Ions in Water and Organic Solvents Investigated Using Molecular Dynamics Simulations: The Swain Acity-Basity Scale Revisited

The asymmetric solvation of ions can be defined as the tendency of a solvent to preferentially solvate anions over cations or cations over anions, at identical ionic charge magnitudes and effective sizes. Taking water as a reference, these effects are quantified experimentally for many solvents by the relative acity (A) and basity (B) parameters of the Swain scale. The goal of the present study is to investigate the asymmetric solvation of ions using molecular dynamics simulations, and to connect the results to this empirical scale. To this purpose, the charging free energies of alkali and halide ions, and of their hypothetical oppositely charged counterparts, are calculated in a variety of solvents. In a first set of calculations, artificial solvent models are considered that present either a charge or a shape asymmetry at the molecular level. The solvation asymmetry, probed by the difference in charging free energy between the two oppositely charged ions, is found to encompass a term quadratic in the ion charge, related to the different solvation structures around the anion and cation, and a term linear in the ion charge, related to the solvation structure around the uncharged ion-sized cavity. For these simple solvent models, the two terms are systematically counteracting each other, and it is argued that only the quadratic term should be retained when comparing the results of simulations involving physical solvents to experimental data. In a second set of calculations, 16 physical solvents are considered. The theoretical estimates for the acity A are found to correlate very well with the Swain parameters, whereas the correlation for B is very poor. Based on this observation, the Swain scale is reformulated into a new scale involving an asymmetry parameter Σ, positive for acitic solvents and negative for basitic ones, and a polarity parameter Π. This revised scale has the same predictive power as the original scale, but it characterizes asymmetry in an absolute sense, the atomistic simulations playing the role of an extra-thermodynamic assumption, and is optimally compatible with the simulation results. Considering the 55 solvents in the Swain set, it is observed that a moderate basity (Σ between -0.9 and -0.3, related to electronic polarization) represents the baseline for most solvents, while a highly variable acity (Σ between 0.0 and 3.0, related to hydrogen-bond donor capacity modulated by inductive effects) represents a landmark of protic solvents.

Hydration Free Energies of Molecular Ions from Theory and Simulation

We present a theoretical/computational framework for accurate calculation of hydration free energies of ionized molecular species. The method is based on a molecular theory, 3D-RISM, combined with a recently developed pressure correction (PC+). The 3D-RISM/PC+ model can provide ∼3 kcal/mol hydration free energy accuracy for a large variety of ionic compounds, provided that the Galvani potential of water is taken into account. The results are compared with direct atomistic simulations. Several methodological aspects of hydration free energy calculations for charged species are discussed.

Meaning and Measurability of Single-Ion Activities, the Thermodynamic Foundations of pH, and the Gibbs Free Energy for the Transfer of Ions between Dissimilar Materials

Considering the relationship between concentration and vapor pressure (or the relationship between concentration and fugacity) single-ion activity coefficients are definable in purely thermodynamic terms. The measurement process involves measuring a contact potential between a solution and an external electrode. Contact potentials are measurable by using thermodynamically reversible processes. Extrapolation of an equation to zero concentration and ionic strength enables determination of single-ion activity coefficients. Single-ion activities can be defined and measured without using any extra-thermodynamic assumptions, concepts, or measurements. This method could serve as a gold standard for the validation of extra-thermodynamic methods for determining single-ion activities. Furthermore, it places the concept of pH on a thermodynamically solid foundation. Contact potential measurements can also be used to determine the Gibbs free energy for the transfer of ions between dissimilar materials.