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Solvation shell

A solvation shell is the layer of solvent molecules that closely surround and interact with a solute particle in a solution, forming a structured region that stabilizes the solute through electrostatic, hydrogen bonding, and other intermolecular forces.^[1] This shell, often the first of multiple concentric layers, consists of solvent molecules acting as nearest neighbors to the solute, with the number of such molecules defined by the solute's coordination number.^[1] In aqueous environments, it is specifically termed the hydration shell, where water molecules orient their dipoles toward charged or polar solutes, such as ions, to minimize the system's free energy.^[2] The structure of the solvation shell is typically characterized using the radial distribution function (RDF), g(r), which describes the probability density of finding a solvent molecule at a distance r from the solute; the first solvation shell is delimited by the position of the first minimum in this function, often around 3–4 Å for small ions in water.^[2] For example, monovalent ions like Na^+ exhibit a coordination number of approximately 5–6 water molecules in their primary shell, while divalent ions like Mg^{2+} coordinate 6, forming octahedral arrangements.^[2] Beyond the first shell lies the second solvation shell, where solvent organization is less pronounced but still influenced by the solute, transitioning gradually to bulk solvent behavior.^[3] These structural features vary with solute size, charge, and solvent type, impacting properties like solubility and reactivity.^[4] Dynamically, the solvation shell is not static but undergoes continuous fluctuations and exchange of solvent molecules, with residence times ranging from picoseconds for non-hydrogen-bonded interactions to nanoseconds in strongly coordinating cases.^[2] Ligand exchange rates, quantified by the number of continuous solvent neighbors (CNS), reveal slower dynamics for multiply charged species due to stronger binding energies.^[2] This motion governs key processes such as ion mobility, proton transfer in water (e.g., via Grotthuss mechanism involving shell reorganization), and the activation barriers for chemical reactions in solution.^[1] In non-aqueous solvents, similar principles apply, but shell composition can include mixed solvents, leading to preferential solvation where one component dominates the shell.^[5] The solvation shell plays a central role in thermodynamic properties, contributing significantly to the free energy of solvation, which determines solubility and phase behavior.^[4] For instance, the enthalpic stabilization from shell formation often competes with entropic costs from solvent ordering, explaining phenomena like the hydrophobic effect where nonpolar solutes induce cage-like ordering in the surrounding water molecules.^[6]^[7] Experimental techniques such as X-ray absorption spectroscopy, neutron scattering, and vibrational spectroscopy, complemented by molecular dynamics simulations, have elucidated these shells in diverse systems, from simple electrolytes to biomolecules. Understanding solvation shells is essential for fields like electrochemistry, where they influence battery electrolyte performance, and biochemistry, where they modulate protein folding and enzyme catalysis.^[8]

Fundamentals

Definition and Formation

A solvation shell refers to the oriented layer of solvent molecules that surrounds a solute ion, molecule, or particle in a solution, arising primarily from electrostatic interactions such as ion-dipole forces, as well as hydrogen bonding and van der Waals attractions.^[4] This structured arrangement stabilizes the solute by compensating for its exposure to the bulk solvent environment.^[9] The formation of the solvation shell begins with the primary shell, which constitutes the first coordination layer of solvent molecules in direct, strong contact with the solute through specific bonding or electrostatic interactions.^[10] Beyond this, the secondary shell emerges via weaker, indirect interactions between the primary shell and adjacent solvent molecules, creating a gradient of influence that diminishes with distance from the solute.^[10] The overall process is driven by the minimization of free energy, where solvent molecules reorient to accommodate the solute's perturbation of the liquid structure. The concept of solvation shells was first systematically described in the early 20th century, notably in the context of ion hydration, by Bernal and Fowler in their 1933 theory of water and ionic solutions.^[11] Key factors influencing shell formation include the solute's size, charge density, and the solvent's polarity. Smaller, highly charged solutes, such as Li⁺, induce tighter primary shells due to stronger electrostatic fields, while larger or less charged species like K⁺ result in more diffuse arrangements.^[9] In polar solvents like water, dipole moments enhance ion-dipole coupling, promoting stable shells; nonpolar solvents, by contrast, yield weaker or absent structuring around charged solutes.^[9] For instance, in aqueous solution, the Na⁺ ion typically coordinates 5–6 water molecules in its primary hydration shell, forming a roughly octahedral geometry that reflects the balance between ionic radius and solvent accessibility.^[12]

Structure and Dynamics

The structure of the solvation shell is characterized by distinct layers of solvent molecules organized around the solute, as revealed by radial distribution functions (RDFs). The RDF, which describes the probability of finding a solvent atom at a given distance from the solute, typically exhibits a sharp first peak corresponding to the primary solvation shell at distances of approximately 2.0–3.5 Å for water oxygen atoms around ions, indicating direct coordination. A second peak, often broader and less intense, appears at 4.0–5.5 Å, delineating the secondary shell where solvent interactions are weaker and more influenced by the primary layer. The coordination number, defined as the average number of solvent molecules in the primary shell obtained by integrating the RDF up to its first minimum, varies with solute type; for example, Li⁺ in water has a coordination number of about 4.1, Na⁺ around 5.5, and K⁺ near 7.0.^[2] These structural features highlight a dense, ordered arrangement in the inner shell that transitions to bulk-like behavior beyond the second shell.^[6] Within the solvation shell, particularly in polar solvents like water, solvent molecules exhibit pronounced orientational order due to interactions with the solute's electric field. Water dipoles align radially around charged solutes, with the degree of alignment increasing with ionic charge density, often quantified by the cosine of the dipole angle relative to the solute-solvent vector (e.g., crossing from random to ordered at cos θ ≈ 0.3). This alignment disrupts the isotropic tetrahedral structure of bulk water, leading to reduced hydrogen bonding in the primary shell—where the average number of H-bonds per water drops below the bulk value of ~3.5—and promotes directional networks that stabilize the shell. In hydration shells around biomolecules or ions, this results in structured motifs like tetrahedral or octahedral arrangements, enhancing local order compared to the bulk solvent's dynamic isotropy.^[13]^[6] The dynamics of solvent molecules in the solvation shell involve characteristic timescales for residence and exchange that differ markedly from bulk solvent. In bulk water, the residence time—related to hydrogen bond lifetimes and reorientational motion—is on the order of 1–2 picoseconds, reflecting rapid molecular tumbling. In contrast, water in the primary solvation shell has longer residence times, typically 10–100 picoseconds or more, due to stronger solute-solvent interactions; for instance, around small cations like Na⁺, times are ~20–50 ps, while in confined sites near proteins or DNA, they extend to hundreds of picoseconds. Exchange rates between the shell and bulk, governed by diffusive jumps, are correspondingly slowed by factors of 2–6 relative to bulk, with some sites showing up to 20-fold retardation, as solvent molecules must overcome energetic barriers to escape the ordered shell.^[14]^[6]^[15] Several factors influence the structure and dynamics of the solvation shell, notably temperature, which modulates shell thickness and transport properties. As temperature increases, RDF peaks broaden slightly, indicating a minor expansion of shell thickness (e.g., first minimum shifting by ~0.1–0.2 Å from 298 K to 318 K), and coordination numbers decrease marginally due to enhanced thermal fluctuations—such as from ~6.2 to 5.9 for Na⁺ in DMF. In shell regions, viscosity is elevated compared to bulk solvent, impeding motion, while diffusion coefficients of solvent molecules are reduced (e.g., ~50–80% of bulk values for water around cations), though still higher than the solute's diffusion, reflecting a semi-confined environment. These effects underscore the shell's role as a dynamic interface sensitive to thermal perturbations.^[16]^[17]^[6]

Theoretical Models

Continuum Models

Continuum models of the solvation shell treat the solvent as a continuous dielectric medium surrounding the solute, neglecting explicit molecular details of the solvent structure. These approaches emerged in the early 20th century to describe electrostatic interactions in electrolyte solutions, providing a macroscopic framework for estimating solvation energies without resolving individual solvent molecules.^[18] The foundational continuum model is the Born solvation model, introduced by Max Born in 1920, which calculates the electrostatic free energy of transferring an ion from vacuum to a solvent. In this model, the ion is represented as a charged sphere of radius r embedded in a dielectric continuum with constant \varepsilon, and the solvation free energy \Delta G is given by

\Delta G = -\frac{N_A z^2 e^2}{8 \pi \varepsilon_0 r} \left(1 - \frac{1}{\varepsilon}\right),

where N_A is Avogadro's number, z is the ion charge number, e is the elementary charge, and \varepsilon_0 is the vacuum permittivity. This equation arises from the difference in the ion's self-energy in vacuum (\varepsilon = 1) and in the solvent, assuming the charge is uniformly distributed on the sphere's surface and the solvation shell forms an abrupt dielectric boundary. The Born model laid the groundwork for modern electrolyte theories by linking solvation energetics to the solvent's dielectric properties, influencing subsequent developments in physical chemistry.^[19]^[18] An extension to polar, non-ionic solutes came with the Onsager reaction field model in 1936, which accounts for the interaction between a solute dipole and the polarized solvent. Here, the solute is placed in a spherical cavity within the continuum solvent, inducing a reaction field that opposes the dipole and provides a self-energy correction to the solvation free energy. This model improves upon the Born approach for molecules with permanent dipoles by incorporating orientational polarization effects, making it suitable for estimating solvation in polar solvents like water.^[20]^[18] Modern continuum models, such as the Polarizable Continuum Model (PCM), extend these ideas by solving the Poisson equation for the solute's electrostatic potential in a polarizable dielectric, accounting for cavity formation and charge distribution on the solute-solvent boundary. PCM and its variants, like Integral Equation Formalism PCM (IEF-PCM), provide more accurate solvation free energies for larger molecules by incorporating nonequilibrium solvation effects and are widely used in quantum mechanical calculations.^[18] Despite their simplicity and utility, continuum models have significant limitations. They ignore the discrete molecular structure of the solvent, leading to inaccuracies for small ions where the solvation shell's atomic-scale organization dominates electrostatic screening. For instance, the Born model often overestimates solvation energies for small ions like Li^+ due to its assumption of a sharp dielectric boundary, which fails to capture enhanced polarization near the solute. Similarly, the Onsager model performs poorly for non-spherical solutes, as its spherical cavity approximation neglects shape-dependent cavity formation and anisotropic polarization. Additionally, these models tend to overestimate solvation effects in low-dielectric solvents, where molecular discreteness and cavity fluctuations become prominent.^[18]^[21]

Discrete and Molecular Models

Discrete and molecular models of the solvation shell treat solvent molecules as distinct entities, enabling detailed descriptions of local interactions and structures that continuum approaches often overlook. These models emphasize atomistic representations to capture the discrete nature of solvation, particularly for ions and small solutes where the first shell dominates energetic contributions. By accounting for individual molecular orientations and packing, they provide insights into shell formation and stability beyond macroscopic dielectric responses. One adsorption-like framework for ion solvation is the Langmuir-inspired model, which analogizes the first coordination shell to a monolayer where solvent molecules adsorb onto the solute surface with saturation limits. In this approach, the local solvent density in the shell is modeled using Langmuir isotherm parameters, such as maximum occupancy correlated with the solute's surface field, allowing predictions of coordination numbers in supercritical or dense fluids. For instance, in supercritical water, this model relates the ratio of bulk to local density in the shell to temperature-independent adsorption strengths, fitting experimental solvation energies with deviations under 5 kJ/mol. Complementary to this, the Blum model within the mean spherical approximation treats the solvation shell as an effective charged shell around ions, incorporating non-additive core exclusions to compute pair correlations and solvation free energies for alkali halides in water, achieving accuracies of 1.5 kJ/mol against data.^[22]^[23] Quasi-lattice theories further describe solvent distribution around solutes through statistical mechanics on a discretized lattice, partitioning the shell into sites occupied by solvent or voids. These models, such as the quasi-lattice quasi-chemical theory, evaluate preferential solvation by balancing solute-solvent and solvent-solvent interactions, predicting shell compositions in binary mixtures via mixing free energies. A notable example is the significant structure theory, which views the liquid as a quasi-lattice blending gas-like and solid-like fractions, applied to electrolyte solutions to model domain-structured water around ions like NaCl, where the shell influences viscosity and diffusion coefficients. Such frameworks highlight how lattice occupancy modulates shell entropy, contrasting with continuum estimates for small-scale systems.^[24]^[25] Integral equation theories, such as the Reference Interaction Site Model (RISM), provide a statistical mechanical approach to compute solvation structures by solving Ornstein-Zernike equations with closure approximations for site-site correlations. RISM captures radial distribution functions and coordination numbers in the solvation shell for molecular solutes in liquids, bridging explicit and implicit descriptions, and is often coupled with quantum mechanics for hybrid models.^[26] Detailed insights into solvation shell properties are obtained through computational simulations, as discussed in the simulation approaches section. For example, studies reveal first hydration shell thicknesses around 3–5 Å for ions in water, with coordination numbers of 5–6 for Na⁺ and slower exchange dynamics compared to bulk solvent. Advanced applications extend these models to complex interactions, such as water-mediated ion pairing and anisotropic solvation around proteins.^[27]^[28]

Applications in Solutions

Electrolyte Solutions

In electrolyte solutions, the solvation shell surrounding ionic solutes plays a crucial role in modulating electrostatic interactions and overall solution behavior. Unlike neutral solutes, ions experience strong orientational ordering of solvent dipoles in their primary solvation shell, which screens the bare charge and influences thermodynamic properties such as activity coefficients. This shell formation is driven by ion-dipole attractions, leading to a structured layer of solvent molecules that extends into secondary shells, affecting ion mobility and interionic distances.^[29] The solvation shell provides a short-range correction to the classical Debye-Hückel (DH) theory, which primarily accounts for long-range electrostatics in dilute solutions. In the extended DH framework, the mean ionic activity coefficient is approximated as \log_{10} \gamma \approx -\frac{0.51 z^2 \sqrt{I}}{1 + \sqrt{I}} (for water at 25°C), where z is the ion charge and I is the ionic strength; however, deviations at higher concentrations arise from finite ion sizes and solvation effects, incorporated via effective hydrated diameters or Born solvation terms that adjust for ion-solvent interactions. These corrections improve predictions of activity coefficients up to ~1 M by modeling the solvation shell's contribution to the excess chemical potential, as seen in optimized models for various salts.^[29]^[30] The solvation number, defined as the average number of solvent ligands in the primary solvation shell of an ion, quantifies the extent of this immediate coordination; for example, the Li^+ ion in water typically coordinates six water molecules, forming an octahedral structure confirmed by neutron scattering. This number is determined experimentally from transport properties like ionic conductivity, where lower mobility of strongly solvated ions (e.g., Li^+ < Na^+) reflects the drag from the shell, or from solubility data, which correlate with hydration energies influencing salt dissolution equilibria. Solvation numbers generally range from 4 to 8 for monovalent ions in aqueous solutions, decreasing with ion size due to reduced charge density.^[31]^[32] Ion pairing in electrolyte solutions is profoundly influenced by solvation shell overlap, leading to distinct speciation patterns. Inner-sphere complexes form when oppositely charged ions directly contact, with one ion replacing a solvent ligand in the other's primary shell, often in low-dielectric solvents or for hard ions; in contrast, outer-sphere complexes maintain separate solvation shells separated by one or more solvent molecules, favored in highly solvating media like water where shell integrity prevents close approach. This distinction affects speciation and reactivity, with shell overlap promoting pairing at higher concentrations and altering effective ion activities.^[33] The Hofmeister series ranks ions by their specific effects on solution properties, attributable to variations in solvation shell strengths; chaotropic ions (e.g., I^-) form weaker, more polarizable shells that disrupt water structure, while kosmotropic ions (e.g., SO_4^{2-}) create rigid, strongly bound shells that enhance water ordering. These differences manifest in ion-specific impacts on protein solubility, where kosmotropes promote salting-out by stabilizing hydrophobic interfaces through indirect shell-mediated effects, without direct protein binding.^[34]

Non-Electrolyte Solutions

In non-electrolyte solutions, solvation shells form around neutral solute molecules through short-range, non-electrostatic interactions, distinguishing them from the charge-dominated structures in electrolyte solutions. These interactions include hydrogen bonding for polar nonelectrolytes, such as urea in water, where the solute's functional groups directly coordinate with solvent molecules, and dispersion forces for nonpolar solutes, leading to weaker and more diffuse shells. The structural characteristics, including hydration numbers and the molar volume of solvent in the shell, show linear dependencies on temperature and concentration up to the complete solvation limit, reflecting the influence of the solute's electric field on solvent dielectric properties without significant differences from electrolytic behavior in basic volumetric terms.^[35] For hydrophobic nonelectrolytes in water, the solvation shell often adopts a clathrate-like structure, as seen with xenon, where water molecules organize into a tetrahedral hydrogen-bonded network enclosing the solute, enhancing bond strengths comparable to those in ice with a redshift of approximately 60 cm⁻¹ in the O-D stretching mode. This ordering, involving 10–15 ice-like hydrogen bonds per solute molecule, extends to nonpolar gases like O₂, whose low solubility arises from hydrophobic hydration effects that increase water's structural rigidity in the first shell without contracting O–O distances, supporting a moderate interpretation of the iceberg model over a rigid clathrate. In nonpolar organic solvents, such as hexane solvating benzene, the shell relies predominantly on London dispersion forces due to comparable molecular polarizabilities, resulting in a loosely structured environment with minimal perturbation to solvent organization and near-ideal mixing behavior.^[36]^[37]^[38] In mixed solvent systems, preferential solvation occurs when the shell composition deviates from the bulk, driven by differential affinities; for instance, in alcohol-water mixtures, nonpolar nonelectrolytes like CO₂ preferentially accumulate alcohol in their shell at low alcohol concentrations, as evidenced by solvation parameters that vary with temperature. This local enrichment is quantified via Kirkwood-Buff integrals (G_{ij}), which relate radial distribution functions to local mole fractions and composition fluctuations, providing insights into size mismatches and deviations from ideality in binary hydrocarbon or alcohol mixtures. Thermodynamic implications include enthalpy contributions from specific interactions like enhanced hydrogen bonding and entropy penalties from shell ordering, which govern solubility; for hydrophobic cases, the negative entropy from structured water dominates, while dispersion-driven solvation in nonpolar media favors enthalpic stabilization with smaller entropic costs. Kirkwood-Buff theory further connects these effects to density fluctuations, enabling prediction of transfer free energies without assuming symmetrical ideality.^[38]^[35]

Biological and Macromolecular Contexts

Protein Hydration Shells

The hydration shell surrounding proteins consists of a vicinal water layer approximately 5-10 Å thick, where water molecules exhibit altered dynamics compared to bulk solvent.^[39] Within this layer, water can be classified as tightly bound, with residence times exceeding nanoseconds due to strong hydrogen bonding with polar or charged protein residues, or diffusive, with shorter residence times on the order of picoseconds to tens of picoseconds, resembling bulk water behavior.^[40]^[6] This heterogeneity arises from the protein surface's chemical composition and topography, leading to a denser packing of water molecules in the first shell, about 15% higher than in bulk water.^[6] The hydration shell plays crucial functional roles in maintaining protein integrity and dynamics. Tightly bound waters stabilize the folded state by bridging hydrogen bonds between protein atoms, contributing to the thermodynamic balance that favors native conformations over unfolded ones.^[41] Diffusive waters in the shell enable structural flexibility, facilitating conformational changes essential for enzymatic activity and ligand binding without rigidifying the protein core.^[41] Disruption of this shell, such as during thermal or chemical denaturation, leads to loss of these stabilizing interactions, promoting unfolding as water access to the hydrophobic core increases.^[41] Experimental studies have quantified the hydration shell's composition using techniques like nuclear magnetic resonance (NMR) and X-ray crystallography. NMR measurements indicate that functional proteins maintain approximately 0.3-0.5 g of water per gram of protein in the shell, corresponding to a monolayer coverage that activates dynamics.^[6] X-ray crystallography of globular proteins typically reveals 200-300 ordered water molecules in the first hydration shell, often located at polar interfaces and contributing to structural resolution.^[42] Evolutionarily, certain hydration shell waters are conserved across homologous proteins, underscoring their structural importance. These conserved waters, identified at ligand-binding interfaces, maintain consistent positions and interactions despite sequence variations, supporting functional specificity.^[43] Cosolvents like urea disrupt shell integrity by displacing water molecules from the first solvation layer, enhancing direct protein-urea contacts and accelerating denaturation.^[44]

Nucleic Acids and Membranes

In nucleic acids, the phosphate backbone is highly hydrated due to its negative charge, with water molecules forming structured layers that stabilize the double helix. Each phosphate group in double-helical DNA coordinates approximately six hydration sites, where water occupancy varies based on the local conformation and sequence.^[45] In A-form DNA, a distinctive "spine of hydration" emerges in the minor groove, consisting of ordered water molecules hydrogen-bonded in a zigzag pattern along the grooves, which contributes to the stability of this compact structure under low-humidity conditions.^[46] This spine involves about two water molecules per base pair and represents a key feature of the first solvation shell, distinguishing A-form from B-form DNA where hydration is more diffuse.^[47] Solvation in the major and minor grooves of nucleic acids plays a critical role in molecular recognition, as water networks mediate interactions with ligands and proteins. Specific patterns of water molecules in the minor groove, such as those forming hydrogen-bonded bridges between bases, determine binding specificity for drugs like netropsin, where displacement of groove waters enhances affinity. In AT-rich sequences, narrower minor grooves support denser hydration shells that influence sequence-specific recognition by transcription factors.^[48] Counterion effects significantly modulate the solvation shell around nucleic acids, particularly through condensation of cations near the phosphate backbone. According to Manning's counterion condensation theory, for DNA with a charge spacing parameter ξ ≈ 4.2 (exceeding 1 for monovalent ions), a layer of condensed Na⁺ ions forms within the first solvation shell, reducing the effective charge and stabilizing the structure against electrostatic repulsion. This condensed layer, typically 5-10 Å thick, competes with water for phosphate coordination, altering the dynamics of the hydration shell and facilitating DNA packaging in vivo. In lipid membranes, the solvation shell manifests as an interfacial water layer at the headgroup region, extending approximately 10 Å from the bilayer surface and comprising 2-3 ordered layers of water molecules. This hydration layer arises from hydrogen bonding between water and polar headgroups like phosphocholine, creating a structured zone that influences membrane fluidity and permeability.^[49] Hydration forces between apposing bilayers repel at short distances (below 20 Å), preventing collapse and maintaining separation; these forces are quantified using the osmotic stress method, where polymer solutions dehydrate multilamellar vesicles to measure pressure versus spacing. Seminal osmotic stress experiments on phosphatidylcholine bilayers reveal an exponential decay of hydration repulsion with a characteristic length of 2-3 Å, underscoring the role of confined water in bilayer stability.^[50] Pathological alterations in solvation shells occur during membrane fusion events, where local dehydration of the interfacial water layer facilitates hemifusion stalks and pore formation. In processes like viral entry or synaptic transmission, proteins such as SNAREs induce transient removal of 1-2 hydration layers, overcoming the repulsive barrier to merge bilayers.^[51] Similarly, amyloid aggregates interacting with membranes disrupt the headgroup hydration shell, promoting lipid extraction and pore formation that exacerbates cellular toxicity in diseases like Alzheimer's.^[52] These changes highlight how perturbed solvation contributes to membrane destabilization in pathological contexts.

Experimental and Computational Methods

Spectroscopic Techniques

Nuclear magnetic resonance (NMR) spectroscopy provides insights into the dynamics and environment of water molecules in the solvation shell through measurements of relaxation times and chemical shifts. The longitudinal (T1) and transverse (T2) relaxation times of protons in shell water are typically shorter than those in bulk water (~3 s at room temperature) due to restricted motion and interactions with the solute, allowing differentiation of hydration layers. For instance, in protein solutions, effective T2 values for hydration water are on the order of 0.1–1 s, reflecting slower rotational correlation times (nanoseconds) compared to bulk water's picosecond regime.^[53] Chemical shift perturbations in NMR spectra arise from the altered magnetic environment in the solvation shell, where water protons experience deshielding or shielding effects from nearby solute atoms, often shifting by several parts per million relative to bulk solvent. These perturbations are particularly evident in studies of ion solvation, such as alkali metal ions, where the first-shell water signals are averaged due to rapid exchange but indicate distinct coordination environments.^[54] Infrared (IR) and Raman spectroscopies probe the vibrational modes of water in the solvation shell, revealing differences in hydrogen bonding compared to bulk water. The O-H stretching vibrations of bound water molecules exhibit red-shifted and broadened peaks around 3200–3400 cm⁻¹, contrasting with the sharper ~3700 cm⁻¹ band of free O-H in bulk water, due to stronger hydrogen bonds in the shell. Raman spectroscopy, in particular, highlights these shifts through enhanced scattering from oriented water dipoles near charged solutes, with peak broadening at ~3400 cm⁻¹ indicating heterogeneous environments in the first hydration layer. For example, in aqueous salt solutions, the low-frequency O-H stretch component intensifies, signaling disrupted tetrahedral ordering in the shell. These techniques are sensitive to temperature and concentration effects, showing how solvation alters collective vibrational coupling. Complementary simulations can validate these spectral assignments by modeling shell-specific frequencies.^[55]^[56] Extended X-ray absorption fine structure (EXAFS) and X-ray absorption near-edge structure (XANES) spectroscopies determine the local atomic structure of solvation shells around metal ions by analyzing X-ray absorption edges. XANES edge shifts reflect changes in oxidation state and coordination geometry in the ion's shell, while EXAFS provides radial distribution functions to quantify bond lengths and coordination numbers. For Cu²⁺ in aqueous solutions, these methods reveal a first shell of 4–6 oxygen atoms at distances of ~1.95–2.0 Å, indicative of distorted octahedral or square-planar coordination influenced by Jahn-Teller distortion. The technique excels in distinguishing inner-shell ligands from outer-sphere water, with Fourier transforms showing peaks corresponding to Cu-O and Cu-Cu distances in concentrated solutions. Such analyses are crucial for understanding ion pairing and shell stability in electrolyte solutions.^[57] Dielectric spectroscopy in the terahertz regime captures the collective dielectric response and reorientational dynamics of water in the solvation shell, which differ from bulk water due to slowed rotational diffusion. In this frequency range (0.1–10 THz), the complex dielectric permittivity reveals Debye-like relaxations for shell water, with relaxation times extended to ~10–20 ps compared to bulk water's ~8 ps, reflecting hindered dipole alignment near solutes. For biomolecular systems, terahertz spectra show reduced absorption in the shell, indicating lower mobility and altered hydrogen-bond networks. This approach quantifies the number of dynamically distinct water layers, often identifying 1–2 shells with progressively recovering bulk-like behavior. These measurements complement vibrational probes by focusing on low-frequency collective modes.^[58]^[59] Neutron scattering techniques, including small-angle neutron scattering (SANS) and inelastic neutron scattering (INS), provide information on the structure and dynamics of solvation shells, particularly sensitive to hydrogen positions. SANS can reveal hydration shell density around proteins or nanoparticles, often showing enhanced density (~10–15% higher than bulk) in the first layer due to favorable interactions. INS probes vibrational and diffusive motions, distinguishing slowed dynamics in the shell (e.g., reduced diffusion coefficients) from bulk. For example, in lysozyme solutions, neutron studies confirm a denser first hydration shell of ~3 Å thickness. These methods are especially useful for isotopic contrast variation to isolate solute-solvent interactions in complex systems.^[60]

Simulation Approaches

Molecular dynamics (MD) simulations provide detailed insights into the structure and dynamics of solvation shells by evolving atomic trajectories under classical force fields. These simulations commonly employ water models such as TIP3P, a three-site rigid model that accurately reproduces liquid water properties and is widely used for studying ion and biomolecular hydration.^[6] Radial distribution functions (RDFs) derived from MD trajectories quantify the probability of finding solvent molecules at specific distances from the solute, defining the first solvation shell up to the first RDF minimum, typically around 3.5 Å for water around ions or proteins.^[6] Residence times, calculated from the autocorrelation of solvent occupancy in the shell, reveal dynamical characteristics; for example, in dilute aqueous NaCl solutions, MD simulations show Na⁺ hydration numbers of approximately 5.5 with shell waters exhibiting exchange dynamics influenced by temperature and density, though specific residence times range from tens to hundreds of picoseconds depending on the ion.^[61] Monte Carlo (MC) methods complement MD by sampling equilibrium configurations of solvation shells in the canonical ensemble, focusing on statistical properties without time evolution. These simulations, often using potentials like SPC for water, generate ensembles for solutes at infinite dilution to explore shell configurations and thermodynamic stability.^[62] Free energy perturbations within MC frameworks compute solvation free energies by gradually scaling interactions, enabling assessment of shell stability; for instance, simulations of hydrophobic and charged butane derivatives in water yield hydration free energies increasing with solute size, highlighting the role of shell reorganization in conformational equilibria.^[62] Ab initio MD simulations offer a quantum mechanical treatment of solvation shells, capturing electronic effects absent in classical approaches, particularly for small systems or reactive environments. Pure ab initio MD, using density functional theory, has been applied to formate ion hydration, revealing RDFs with fewer hydrogen bonds per oxygen than classical predictions and average first-shell hydration numbers aligning with experiments.^[63] Hybrid quantum mechanics/molecular mechanics (QM/MM) variants extend this to larger systems like proteins by treating the solute and inner shell quantum mechanically while modeling the outer environment classically; for Mg²⁺ in water, QM/MM MD simulations demonstrate a stable octahedral first shell of six waters with picosecond-scale exchange and distortions up to 20° in O-Mg-O angles. Recent advances since 2020 incorporate machine learning potentials (MLPs) to accelerate large-scale solvation shell simulations, achieving quantum-level accuracy at classical speeds. These potentials, trained on ab initio data, model explicit solvent interactions for chemical processes; for example, MLPs have enabled simulations of Diels-Alder reactions in water/methanol, revealing solvent effects on free energy barriers reduced by 2.4 kcal/mol due to hydrophobic shell stabilization.^[64] Active learning strategies minimize training data needs, facilitating studies of ion dynamics and shell structures in concentrated electrolytes. Such predictions can be validated against spectroscopic observables like vibrational frequencies.^[64]

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[PDF] Solute/Solvent Interactions (Theoretical and Computational ...
The. Born-Kirkwood-Onsager model would require the electrostatic portion of the free energy of solvation for these molecules to be identically zero.<|control11|><|separator|>
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Ion Solvation in Supercritical Water Based on an Adsorption Analogy
The model utilizes two parameters: a maximum local density, which is found to be insensitive to temperature and correlated with the surface field, and a ...
[22]
[PDF] A Simple Model for Ion Solvation with Non Additive Cores - DTIC
the pair correlation functions can be derived from a simple model in which the ions are replaced by charged shells and the dipoles by charged dipolar shells.
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Preferential solvation in binary mixtures. Comparison between the ...
The quasi-lattice quasi-chemical (QLQC) model and the stepwise solvent exchange (SSE) model are both used in solvation chemistry to describe preferential ...Missing: theory | Show results with:theory
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Significant structure theory applied to electrolyte solution - PubMed
The significant structure theory has been successfully applied to an aqueous NaCl solution. Liquid water is assumed to have a domain structure.Missing: solvation | Show results with:solvation
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Solvation Structure and Energetics of Single Ions at the Aqueous ...
For this analysis, we define the first solvation shell cutoff distance as the position of the first minimum in the radial distribution function for single ions ...
[26]
Water-Mediated Ion Pairing: Occurrence and Relevance
We discuss the importance of specific ion-pairing interactions between cations like Li+ and Na+ and anionic carboxylate and phosphate groups for the structure ...
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A shell-resolved analysis of preferential solvation of coffee ...
Feb 7, 2018 · Schematic view of solvation shells around an anisotropic solute. The white polyhedra in the dark red region correspond to the Voronoi shell ...
[28]
Corrected Debye−Hückel Theory of Salt Solutions: Size Asymmetry and Effective Diameters
### Summary of Solvation Shells and Short-Range Interactions in Corrected Debye-Hückel Theory
[29]
An analysis of the parameters in the Debye-Hückel theory
Three different activity coefficient models are analyzed and compared for 14 salt systems in order to have a more complete picture of the capabilities and ...
[30]
The Hydration Number of Li+ in Liquid Water - ACS Publications
Neutron scattering measurements on LiCl solutions in liquid water have led to a firm conclusion that the Li + ion has six near-neighbor water molecule partners.
[31]
Solvation Number - an overview | ScienceDirect Topics
Solvation number represents the number of molecules that remain associated with the ion during its movement through the solution. The solvation number is more ...
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Ion Pairing | Chemical Reviews - ACS Publications
Ion pairing describes the (partial) association of oppositely charged ions in electrolyte solutions to form distinct chemical species called ion pairs.
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Hofmeister Series of Ions: A Simple Theory of a Not So Simple Reality
Dec 19, 2013 · Ion-specific effects on salting-in and salting-out of proteins, protein denaturation, as well as enzymic activity are typically rationalized in ...
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Solvation of Electrolytes and Nonelectrolytes in Aqueous Solutions
### Summary of Solvation of Nonelectrolytes in Aqueous Solutions
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Origin of hydrophobicity and enhanced water hydrogen bond ...
Dec 27, 2016 · We present unequivocal experimental proof for strengthened water hydrogen bonds near purely hydrophobic solutes, matching those in ice and clathrates.
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Water's Structure around Hydrophobic Solutes and the Iceberg Model
Jan 29, 2013 · The structure of water in the hydration shells of small hydrophobic solutes was investigated through molecular dynamics.
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A Study on Kirkwood−Buff Integrals and Preferential Solvation in ...
Analysis of the pressure effect on the local composition in a water-alkanol mixture using Kirkwood-Buff integrals. Journal of Structural Chemistry 2014, 55 ...
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Protein Hydration Dynamics: Much Ado about Nothing?
Oct 5, 2017 · (3, 6) Because proteins are large molecules, they can contain more than 1000 water molecules within a thin layer of ∼5Å around its folded state.
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https://pubs.acs.org/doi/10.1021/acs.jpclett.7b02324
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Water Determines the Structure and Dynamics of Proteins
High-resolution experimental techniques, like X-ray crystallography, can determine the position and sometimes orientation of strongly bound water molecules. In ...
[41]
Water polygons in high-resolution protein crystal structures - NIH
Average number of waters per molecular weight of protein is 11.8 kDa−1 with a standard deviation of 3.9 kDa−1. This shows that on an average of 12 water ...
[42]
Hydration in Drug Design. 3. Conserved Water Molecules ... - PubMed
If water molecules are conserved at the ligand-binding sites of homologous proteins, such a finding may suggest the structural importance of water molecules in ...
[43]
Urea denaturation by stronger dispersion interactions with proteins ...
Nov 4, 2008 · In the first step, urea displaces the water molecules within the first solvation shell of the protein that allows it to bind tighter with ...Missing: source | Show results with:source
[44]
Hydration of the Phosphate Group in Double-Helical DNA
It is shown that the waters are concentrated in six hydration sites per phosphate and that the positions and occupancies of these sites are dependent on the ...
[45]
DNA's Chiral Spine of Hydration | ACS Central Science
May 24, 2017 · This chiral spine of hydration is templated by the helical structure and provides a direct label-free probe of the solvation shell.
[46]
Chiral SFG spectroscopy detects DNA first hydration shell and base ...
Sep 4, 2024 · This “spine of hydration” comprises ∼2 water molecules per base pair3 of double-stranded DNA (dsDNA) and accounts for around 3%–6% of the first ...
[47]
A Role for Water Molecules in DNA−Ligand Minor Groove ...
Targeting the minor groove of DNA through binding to a small molecule has long been considered an important molecular-recognition strategy in biology.Missing: affecting | Show results with:affecting
[48]
Structured Water Layers Adjacent to Biological Membranes - PMC
Two regions of the water correspond to a first and second solvation shell surrounding the phosphocholine groups. The extent of lipid hydration is also revealed ...Missing: stress | Show results with:stress
[49]
Direct Imaging of Individual Intrinsic Hydration Layers on Lipid ...
The osmotic stress measurements by McIntosh and Simon have suggested that the hydration force dominates the short-range interaction force if the bilayer ...
[50]
SNARE-mediated membrane fusion trajectories derived from force ...
Fusion of lipid bilayers is usually prevented by large energy barriers arising from removal of the hydration shell, formation of highly curved structures, ...
[51]
Amyloid-Mediated Mechanisms of Membrane Disruption - MDPI
Many reports suggest that the toxic properties of amyloid aggregates are correlated with their ability to damage cell membranes. However, the molecular ...
[52]
Assessing the Validity of NMR Relaxation Rates Obtained from ...
Jun 16, 2023 · The MD simulations of the 1H NMR relaxation times T1,2 in the fast motion regime where T1 = T2 agree with measured (de-oxygenated) T2 data ...
[53]
Solvent Relaxation NMR Measurements on Polymer, Particle ...
In this paper the PEO/SDS/silica systems are examined using solvent relaxation nuclear magnetic resonance spectroscopy measurements which can give information ...
[54]
[PDF] Nuclear Magnetic Resonance Studies of the Solvation Structures of ...
those in solvation shells, where the exchange frequency is beyond the NMR detection time scale, leading to an averaged peak position for each carbon atoms ...Missing: spectroscopy T2
[55]
First-Principles Calculation of 1H NMR Chemical Shifts of Complex ...
Nov 23, 2020 · Probing the Solvent Shell with 195Pt Chemical Shifts: Density Functional Theory Molecular Dynamics Study of PtII and PtIV Anionic Complexes ...
[56]
Vibrational Coupling and Hydrogen-Bond Structure of Water in the ...
Aug 2, 2023 · Hydration shell spectroscopy in HOD unambiguously shows that the average H-bonding of water becomes stronger in the HS than that of bulk water.
[57]
Two-dimensional infrared-Raman spectroscopy as a probe ... - Nature
Apr 7, 2023 · Finally, we note that a peak around (400 cm−1, 3700 cm−1) appears at elevated temperature, while the other peak at about (700 cm−1, 3400 cm−1) ...
[58]
EXAFS Study on the Coordination Chemistry of the Solvated Copper ...
Jul 2, 2020 · The aim of this study is to collect high-quality EXAFS data to high k values of solvated copper(II) ions in solution in series of oxygen donor ...
[59]
Time-resolved terahertz–Raman spectroscopy reveals that cations ...
Jun 30, 2022 · The solvation of ions changes the physical, chemical and thermodynamic properties of water, and the microscopic origin of this behaviour is ...
[60]
Terahertz Spectra and Hydration Dynamics of KNO 3 and K 2 SO 4 ...
Aug 19, 2025 · On the dynamical side, ultrafast IR spectroscopy has been widely used to track the reorientation and vibrational lifetimes of water molecules in ...
[61]
Molecular dynamics simulation study of ionic hydration and ion ...
In the present study, we carried out molecular dynamics simulations of aqueous NaCl solutions at both infinite dilution and rather high concentration (1 molal) ...Original Articles · 3. Infinitely Dilute... · 3.3. Hydration Shell...
[62]
Hydration and Conformational Equilibria of Simple Hydrophobic and ...
Canonical ensemble Monte Carlo (MC) simulations (Allen and Tildesley, 1987) of one solute molecule at infinite dilution in water were performed at a ...
[63]
Ab Initio Molecular Dynamics Study of Formate Ion Hydration
Ab initio QM/MM approaches generally apply either Hartree−Fock (HF) or density functional theory (DFT) to treat the solute. In virtually all ab initio QM/MM ...
[64]
Modelling chemical processes in explicit solvents with machine ...
Jul 20, 2024 · Here, we present a general strategy for generating reactive machine learning potentials to model chemical processes in solution.