Elucidating and contrasting the mechanisms for Mg and Ca sulfate ion-pair formation with multi-level embedded quantum mechanics/molecular dynamics simulations

Solutions and minerals containing sulfate (SO42-), and Ca2+ and Mg2+ cations, are ubiquitous throughout the lithosphere and are significant components of seawater, thus presenting a prototypical system for the study of strong electrolytes and crystal nucleation mechanisms. However, despite their relative abundance, key questions remain unanswered about the most fundamental atomic-level steps of their mineralization pathways and aqueous dynamics. Here, we carry out enhanced sampling multi-level molecular dynamics (MD) embedded correlated wavefunction theory simulations to elucidate ion-pairing mechanisms for Mg-SO4 and Ca-SO4 in concentrated aqueous solution, accurately capturing effects arising from both structural dynamics and electron exchange-correlation. We predict contact-ion-pair formation to be barrierless and highly exoergic for Ca-SO4, in agreement with its minimal solubility, whereas for Mg-SO4, solvent-shared and contact ion pairs have similar free energies, qualitatively consistent with its higher solubility. Finally, we demonstrate that brief high-temperature pre-equilibration may be utilized to accelerate convergence of free energies in blue-moon-ensemble enhanced-sampling MD.

Ion-Pairing Propensity in Guanidinium Salts Dictates Their Protein (De)stabilization Behavior

Since the proposition of the Hofmeister series, guanidinium (Gdm) salts hold a special mention in protein science owing to their contrasting effect on protein(s) depending on the counteranion(s). For example, while GdmCl is known to act as a potential protein denaturant, Gdm2SO4 offers minimal effect on protein structure. Despite the fact that theoretical studies reckon the formation of ion-pairing to be responsible for such behavior, experimental validation of this hypothesis is still in sparse. In this study, we combine electrochemical impedance spectroscopy (EIS) and THz spectroscopy to underline the effect of GdmCl and Gdm2SO4 on a model amide molecule N-methylacetamide (NMA). Molecular dynamics (MD) simulation studies predict that Gdm2SO4 forms heteroion pairing in water, which inhibits Gdm+ ions to approach NMA molecules, while in case of GdmCl, Gdm+ ions directly interact with NMA. The experimental findings on ion hydration, specifically the detailed analysis of the ion-water rattling mode, which appears in the THz frequency domain, unambiguously endorse this hypothesis. Our study establishes the fact that the propensity of ion-pairing in Gdm salts dictates their (de)stabilization effect on proteins.

Theoretical and practical investigation of ion-ion association in electrolyte solutions

In this study, we present a new equation of state for electrolyte solutions, integrating the statistical associating fluid theory for variable range interactions utilizing the generic Mie form and binding Debye-Hückel theories. This equation of state underscores the pivotal role of ion-ion association in determining the properties of electrolyte solutions. We propose a unified framework that simultaneously examines the thermodynamic properties of electrolyte solutions and their electrical conductivity, given the profound impact of ion pairing on this transport property. Using this equation of state, we predict the liquid density, mean ionic activity coefficient, and osmotic coefficient for binary NaCl, Na2SO4, and MgSO4 aqueous solutions at 298.15 K. Additionally, we evaluate the molar conductivity of these systems by considering the fraction of free ions derived from our equation of state in conjunction with two advanced electrical conductivity models. Our results reveal that, while ion-ion association has a minimal influence on the modification of the predicted properties of sodium chloride solutions, their impact on sodium and magnesium sulfate solutions is considerably more noticeable.

Terahertz spectroscopy of thick and diluted water solutions

While bright terahertz sources are used to perform nonlinear experiments, they can be advantageous for high-precision linear measurements of opaque samples. By placing the sample away from the focus, nonlinearities can be suppressed, and sizeable amounts of transmitted radiation detected. Here, this approach is demonstrated for a 0.5 mm thick layer of liquid water in a static sample holder. Variations of the index of refraction as small as (7 ± 2) · 10-4 were detected at 0.58 THz for an aqueous salt solution containing ten millimoles of sodium chloride. To my knowledge, this precision is unprecedented in time-domain spectroscopy studies of diluted aqueous systems or other optically thick and opaque materials.

Physical insight into the entropy-driven ion association

The ion association is widely believed to be dominated by the favorable entropy change arising from the release of water molecules from ion hydration shells. However, no direct thermodynamic evidence exists to validate the reliability and suitability of this view. Herein, we employ complicated free energy calculations to rigorously split the free energy including its entropic and enthalpic components into the water-induced contributions and ion-ion interaction terms for several ion pairs from monatomic to polyatomic ions, spanning the size range from small kosmotropes to large chaotropes (Na⁺ , Cs⁺ , Ca²⁺ , F^- , I^- , CO₃ ^2- , and HPO₄ ^2- ). Our results successfully reveal that though ion associations are indeed determined by a delicate balance between the favorable entropy variation and the repulsive enthalpy change, the entropy gain dominated by the solvent occurs only for the monatomic ion pairing. The water-induced entropic contribution significantly goes against the ion pairing between polyatomic anion and cation, which is, alternatively, dominated by the favorable entropy from the ion-ion interaction term, due to the configurational arrangement of polyatomic anions involved in ion association. The structural and dynamic analysis demonstrates that the entropy penalty from the water phase is primarily ascribed to the enhanced stability of water molecules around the cation imposed by the incoming anion. Our study successfully provides a fundamental understanding of water-mediated ion associations and highlights disparate lengthscale dependencies of the dehydration thermodynamics on the specific types of ions.

Time-resolved terahertz-Raman spectroscopy reveals that cations and anions distinctly modify intermolecular interactions of water

The solvation of ions changes the physical, chemical and thermodynamic properties of water, and the microscopic origin of this behaviour is believed to be ion-induced perturbation of water's hydrogen-bonding network. Here we provide microscopic insights into this process by monitoring the dissipation of energy in salt solutions using time-resolved terahertz-Raman spectroscopy. We resonantly drive the low-frequency rotational dynamics of water molecules using intense terahertz pulses and probe the Raman response of their intermolecular translational motions. We find that the intermolecular rotational-to-translational energy transfer is enhanced by highly charged cations and is drastically reduced by highly charged anions, scaling with the ion surface charge density and ion concentration. Our molecular dynamics simulations reveal that the water-water hydrogen-bond strength between the first and second solvation shells of cations increases, while it decreases around anions. The opposite effects of cations and anions on the intermolecular interactions of water resemble the effects of ions on the stabilization and denaturation of proteins.

Specific Ion Effects in Different Media: Current Status and Future Challenges

We discuss the current state of research as well as the future challenges for a deeper understanding of specific ion effects in protic and aprotic solvents as well as various additional media. Despite recent interest in solute or interfacial effects, we focus exclusively on the specific properties of ions in bulk electrolyte solutions. Corresponding results show that many mechanisms remain unknown for these simple media, although theoretical, computational, and experimental studies have provided some insights into explaining individual observations. In particular, the importance of local interactions and electronic properties is emphasized, which enabled a more consistent interpretation of specific ion effects over the past years. Despite current insufficient knowledge, we also discuss future challenges in relation to dynamic properties as well as the influence of different concentrations, different solvents, and solute contributions to gain a deeper understanding of specific ion effects for technological applications.

Proteins maintain hydration at high [KCl] concentration regardless of content in acidic amino acids

Proteins of halophilic organisms, which accumulate molar concentrations of KCl in their cytoplasm, have a much higher content in acidic amino acids than proteins of mesophilic organisms. It has been proposed that this excess is necessary to maintain proteins hydrated in an environment with low water activity, either via direct interactions between water and the carboxylate groups of acidic amino acids or via cooperative interactions between acidic amino acids and hydrated cations. Our simulation study of five halophilic proteins and five mesophilic counterparts does not support either possibility. The simulations use the AMBER ff14SB force field with newly optimized Lennard-Jones parameters for the interactions between carboxylate groups and potassium ions. We find that proteins with a larger fraction of acidic amino acids indeed have higher hydration levels, as measured by the concentration of water in their hydration shell and the number of water/protein hydrogen bonds. However, the hydration level of each protein is identical at low (b_KCl = 0.15 mol/kg) and high (b_KCl = 2 mol/kg) KCl concentrations; excess acidic amino acids are clearly not necessary to maintain proteins hydrated at high salt concentration. It has also been proposed that cooperative interactions between acidic amino acids in halophilic proteins and hydrated cations stabilize the folded protein structure and would lead to slower dynamics of the solvation shell. We find that the translational dynamics of the solvation shell is barely distinguishable between halophilic and mesophilic proteins; if such a cooperative effect exists, it does not have that entropic signature.

Hydrogen-Bond Structure and Low-Frequency Dynamics of Electrolyte Solutions: Hydration Numbers from ab Initio Water Reorientation Dynamics and Dielectric Relaxation Spectroscopy

We present an atomistic simulation scheme for the determination of the hydration number (h) of aqueous electrolyte solutions based on the calculation of the water dipole reorientation dynamics. In this methodology, the time evolution of an aqueous electrolyte solution generated from ab initio molecular dynamics simulations is used to compute the reorientation time of different water subpopulations. The value of h is determined by considering whether the reorientation time of the water subpopulations is retarded with respect to bulk-like behavior. The application of this computational protocol to magnesium chloride (MgCl2 ) solutions at different concentrations (0.6-2.8 mol kg-1 ) gives h values in excellent agreement with experimental hydration numbers obtained using GHz-to-THz dielectric relaxation spectroscopy. This methodology is attractive because it is based on a well-defined criterion for the definition of hydration number and provides a link with the molecular-level processes responsible for affecting bulk solution behavior. Analysis of the ab initio molecular dynamics trajectories using radial distribution functions, hydrogen bonding statistics, vibrational density of states, water-water hydrogen bonding lifetimes, and water dipole reorientation reveals that MgCl2 has a considerable influence on the hydrogen bond network compared with bulk water. These effects have been assigned to the specific strong Mg-water interaction rather than the Cl-water interaction.

Restructuring of Hydration Shell Water due to Solvent-Shared Ion Pairing (SSIP): A Case Study of Aqueous MgCl2 and LaCl3 Solutions

Hydration of ions plays a crucial role in interionic interactions and associated processes in aqueous media, but selective probing of the hydration shell water is nontrivial. Here, we introduce Raman difference with simultaneous curve fitting (RD-SCF) analysis to extract the OH-stretch spectrum of hydration shell water, not only for the fully hydrated ions (Mg²⁺, La³⁺, and Cl^-) but also for the ion pairs. RD-SCF analyses of diluted MgCl₂ (0.18 M) and LaCl₃ (0.12 M) solutions relative to aqueous NaCl of equivalent Cl^- concentrations provide the OH-stretch spectra of water in the hydration shells of fully hydrated Mg²⁺ and La³⁺ cations relative to that of Na⁺. Integrated intensities of the hydration shell spectra of Mg²⁺ and La³⁺ ions increase linearly with the salt concentration (up to 2.0 M MgCl₂ and 1.3 M LaCl₃), which suggests no contact ion pair (CIP) formation in the MgCl₂ and LaCl₃ solutions. Nevertheless, the band shapes of the cation hydration shell spectra show a growing signature of Cl^--associated water with the rising salt concentration, which is a manifestation of the formation of a solvent-shared ion pair (SSIP). The OH-stretch spectrum of the shared/intervening water in the SSIP, retrieved by second-round RD-SCF analysis (2RD-SCF), shows that the average H-bonding of the shared water is weaker than that of the hydration water of the fully hydrated cation (Mg²⁺ or La³⁺) but stronger than that of the anion (Cl^-). The shared water displays an overall second-order dependence on the concentration of the interacting ions, unveiling 1:1 stoichiometry of the SSIP formed between Mg²⁺ and Cl^- as well as La³⁺ and Cl^-.

Micro-Raman and density functional theory analyses of ion pairs in concentrated sodium tetrahydroxyborate droplets

In this study, ion pairs in a single sodium tetrahydroxyborate [Na [B(OH)₄] droplet were analyzed using an "in-situ strategy" in which a sample-droplet of nanogram mass was deposited on a hydrophobic substrate and droplet was forced to enter into a supersaturated state by decreasing the relative humidity (RH) of the environment. The structure of the solvated [B(OH)₄^-] ionic moiety with various molar water-to-solute ratios (WSR) was analyzed using Raman spectroscopy. To confirm the structural changes in the droplet, electronic structure calculations were carried out using density functional theory (DFT). The frequencies calculated for the totally symmetric BO stretching vibration (v_sym(BO)) of the [B(OH)₄^-] moiety were compared with those of the fundamental bands observed in the Raman spectra recorded of the droplets. The following results have been obtained: (i) when WSR is reduced from 9 to 0.1, the frequency of the band that corresponds to v_sym(BO) shifts from 745 to 746 cm^-1, and its full-width at half-maximum value increases from 19.7 to 20.5 cm^-1; (ii) when WSR ≥7, the solvent-shared ion pair (SIP) is predominantly present in the solution, whereas in the case of WSR < 7, SIP transforms into a contact ion pair (CIP) formed by Na⁺ and [B(OH)₄^-] in bidentate coordination; (iii) when WSR = 3, most of the CIPs transform into a cationic type of triple ion pair (TIP) composed of two Na⁺ and one [B(OH)₄^-] in bidentate coordination; (iv) when WSR is further reduced, most TIP continually associate to form a more complex structure and with a small amount of six-membered ring complex also formed. These results will help us understand the ion association mechanism during dehydration process of Na[B(OH)₄] droplets.

Cooperativity and ion pairing in magnesium sulfate aqueous solutions from the dilute regime to the solubility limit

A combined THz and simulation study on MgSO₄ find no contact ion pairs in highly concentrated solutions.

The pore solution of cement-based materials: structure and dynamics of water and ions from molecular simulations

Diffusion processes are crucial to the durability and confinement capacity of cement-based materials as well as property development. The liquid phase in cement-based materials is the pore solution, whose composition changes with age and is a function of the cement system composition. Water structure and dynamics are recognized to be affected by the presence of ions. Fundamental understanding of the physical processes underlying these changes can be critical in the elucidation of the physical origin of durability issues and in the development of new admixtures. Here, the structure and dynamics of water and ions present in pore solutions are studied using molecular dynamics simulations. Self-diffusion coefficients are computed for bulk solutions mimicking the complex composition of pore solutions. Specific ion effects on water dynamics are interpreted in terms of water reorientation time. The composition dependency of ion dynamics explains the evolution of the ionic conductivity of the pore solutions.

Ion Hydration and Ion Pairing as Probed by THz Spectroscopy

Ion hydration is of pivotal importance for many fundamental processes. Various spectroscopic methods are used to study the retardation of the hydration bond dynamics in the vicinity of anions and cations. Here we introduce THz-FTIR spectroscopy as a powerful method to answer the open questions. We show through dissection of THz spectra that we can pinpoint characteristic absorption features that can be attributed to the rattling modes of strongly hydrating ions within their hydration cages as well as vibrationally induced charge fluctuations in the case of weakly hydrating ions. Further analysis yields information on anion-cation cooperativity, the size of the dynamic hydration shell, as well as the lifetimes of these collective ion-hydration water modes and their connecting thermal bath states. Our study provides evidence for a non-additive behavior, thus questioning the simplified Hofmeister model. THz spectroscopy enables ion pairing to be observed and quantified at a high salt concentration.

Developing force fields when experimental data is sparse: AMBER/GAFF-compatible parameters for inorganic and alkyl oxoanions

We present a set of Lennard-Jones parameters for classical, all-atom models of acetate and various alkylated and non-alkylated forms of sulfate, sulfonate and phosphate ions, optimized to reproduce their interactions with water and with the physiologically relevant sodium, ammonium and methylammonium cations. The parameters are internally consistent and are fully compatible with the Generalized Amber Force Field (GAFF), the AMBER force field for proteins, the accompanying TIP3P water model and the sodium model of Joung and Cheatham. The parameters were developed primarily relying on experimental information - hydration free energies and solution activity derivatives at 0.5 m concentration - with ab initio, gas phase calculations being used for the cases where experimental information is missing. The ab initio parameterization scheme presented here is distinct from other approaches because it explicitly connects gas phase binding energies to intermolecular interactions in solution. We demonstrate that the original GAFF/AMBER parameters often overestimate anion-cation interactions, leading to an excessive number of contact ion pairs in solutions of carboxylate ions, and to aggregation in solutions of divalent ions. GAFF/AMBER parameters lead to excessive numbers of salt bridges in proteins and of contact ion pairs between sodium and acidic protein groups, issues that are resolved by using the optimized parameters presented here.

Is the Solution Activity Derivative Sufficient to Parametrize Ion-Ion Interactions? Ions for TIP5P Water

Biomolecular processes involve hydrated ions, and thus molecular simulations of such processes require accurate force-field parameters for these ions. In the best force-fields, both ion-water and anion-cation interactions are explicitly parametrized. First, the ion Lennard-Jones parameters are optimized to reproduce, for example, single ion solvation free energies; then ion-pair interactions are adjusted to match experimental activity or activity derivatives. Here, we apply this approach to derive optimized parameters for concentrated NaCl, KCl, MgCl₂, and CaCl₂ salt solutions, to be used with the TIP5P water model. These parameters are of interest because of a number of desirable properties of the TIP5P water model, especially for the simulation of carbohydrates. The results show, that this state of the art approach is insufficient, because the activity derivative often reaches a plateau near the target experimental value, for a wide range of parameter values. The plateau emerges from the interconversion between different types of ion pairs, so parameters leading to equally good agreement with the target solution activity or activity derivative yield very different solution structures. To resolve this indetermination, a second target property, such as the experimentally determined ion-ion coordination number, is required to uniquely determine anion-cation interactions. Simulations show that combining activity derivatives and coordination number as experimental target properties to parametrize ion-ion interactions, is a powerful method for reliable ion-water force field parametrization, and gives insight into the concentration of contact or solvent shared ion pairs in a wide range of salt concentrations. For the alkali and halide ions Li⁺, Rb⁺, Cs⁺, F^-, Br^-, and I^-, we present ion-water parameters appropriate at infinite dilution only.