On the microscopic fluctuations driving the NMR relaxation of quadrupolar ions in water

Electrical noise in electrolytes: a theoretical perspective

Seemingly unrelated experiments such as electrolyte transport through nanotubes, nano-scale electrochemistry, NMR relaxometry and surface force balance measurements, all probe electrical fluctuations: of the electric current, the charge and polarization, the field gradient (for quadrupolar nuclei) and the coupled mass/charge densities. The fluctuations of such various observables arise from the same underlying microscopic dynamics of the ions and solvent molecules. In principle, the relevant length and time scales of these dynamics are encoded in the dynamic structure factors. However, modelling the latter for frequencies and wavevectors spanning many orders of magnitude remains a great challenge to interpret the experiments in terms of physical processes such as solvation dynamics, diffusion, electrostatic and hydrodynamic interactions between ions, interactions with solid surfaces, etc. Here, we highlight the central role of the charge-charge dynamic structure factor in the fluctuations of electrical observables in electrolytes and offer a unifying perspective over a variety of complementary experiments. We further analyze this quantity in the special case of an aqueous NaCl electrolyte, using simulations with explicit ions and an explicit or implicit solvent. We discuss the ability of the standard Poisson-Nernst-Planck theory to capture the simulation results, and how the predictions can be improved. We finally discuss the contributions of ions and water to the total charge fluctuations. This work illustrates an ongoing effort towards a comprehensive understanding of electrical fluctuations in bulk and confined electrolytes, in order to enable experimentalists to decipher the microscopic properties encoded in the measured electrical noise.

Unified Description of Proton NMR Relaxation in Water, Acetonitrile, and Methane from Molecular Dynamics Simulations in the Liquid, Supercritical, and Gas Phases

A comprehensive calculation of proton NMR relaxation in water, acetonitrile, and methane across a wide range of the phase diagram is provided via ab initio and force-field-based molecular dynamics simulations. The formalism used for the spin-rotation (SR) contribution to relaxation is developed for use with any molecular symmetry and utilizes the full molecular SR tensors, which are calculated from first-principles via Kohn-Sham (KS) DFT. In combination with calculations of the dipolar contribution, near-quantitative agreement with total measured relaxation rates is achieved.

Quadrupolar 23Na+ NMR relaxation as a probe of subpicosecond collective dynamics in aqueous electrolyte solutions

Nuclear magnetic resonance relaxometry represents a powerful tool for extracting dynamic information. Yet, obtaining links to molecular motion is challenging for many ions that relax through the quadrupolar mechanism, which is mediated by electric field gradient fluctuations and lacks a detailed microscopic description. For sodium ions in aqueous electrolytes, we combine ab initio calculations to account for electron cloud effects with classical molecular dynamics to sample long-time fluctuations, and obtain relaxation rates in good agreement with experiments over broad concentration and temperature ranges. We demonstrate that quadrupolar nuclear relaxation is sensitive to subpicosecond dynamics not captured by previous models based on water reorientation or cluster rotation. While ions affect the overall water retardation, experimental trends are mainly explained by dynamics in the first two solvation shells of sodium, which contain mostly water. This work thus paves the way to the quantitative understanding of quadrupolar relaxation in electrolyte and bioelectrolyte systems.

Simulations of electric field gradient fluctuations and dynamics around sodium ions in ionic liquids

The T₁ relaxation time measured in nuclear magnetic resonance experiments contains information about electric field gradient (EFG) fluctuations around a nucleus, but computer simulations are typically required to interpret the underlying dynamics. This study uses classical molecular dynamics (MD) simulations and quantum chemical calculations, to investigate EFG fluctuations around a Na⁺ ion dissolved in the ionic liquid 1-ethyl 3-methylimidazolium tetrafluoroborate, [Im₂₁][BF₄], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na⁺ in [Im₂₁][BF₄], and the anti-shielding coefficient is comparable to its value in water. EFG correlation functions, C_EFG(t), calculated using quantum mechanical methods or from force field charges are roughly equivalent after 200 fs, supporting the use of classical MD for estimating T₁ times of monatomic ions in this ionic liquid. The EFG dynamics are strongly bi-modal, with 75%-90% of the de-correlation attributable to inertial solvent motion and the remainder to a highly distributed diffusional processes. Integral relaxation times, ⟨τ_EFG⟩, were found to deviate from hydrodynamic predictions and were non-linearly coupled to solvent viscosity. Further investigation showed that Na⁺ is solvated by four tetrahedrally arranged [BF₄]^- anions and directly coordinated by ∼6 fluorine atoms. Exchange of [BF₄]^- anions is rare on the 25-50 ns timescale and suggests that motion of solvent-shell [BF₄]^- is the primary mechanism for the EFG fluctuations. Different couplings of [BF₄]^- translational and rotational diffusion to viscosity are shown to be the source of the non-hydrodynamic scaling of ⟨τ_EFG⟩.

Insights into the Effect of Lithium Doping on the Deep Eutectic Solvent Choline Chloride:Urea

Choline-based deep eutectic solvents (DESs) are potential candidates to replace flammable organic solvent electrolytes in lithium-ion batteries (LIBs). The effect of the addition of a lithium salt on the structure and dynamics of the material needs to be clarified before it enters the battery. Here, the archetypical DES choline chloride:urea at 1:2 mole fraction has been added with lithium chloride at two different concentrations and the effect of the additional cation has been evaluated with respect to the non-doped system via multinuclear NMR techniques. ¹H and ⁷Li spin-lattice relaxation times and diffusion coefficients have been measured between 298 K and 373 K and revealed a decrease in both rotational and translational mobility of the species after LiCl doping at a given temperature. Temperature dependent ³⁵Cl linewidths reflect the viscosity increase upon LiCl addition, yet keep track of the lithium complexation. Quantitative indicators such as correlation times and activation energies give indirect insights into the intermolecular interactions of the mixtures, while lithium single-jump distance and transference number shed light into the lithium transport, being then of help in the design of future DES electrolytes.

NMR Relaxation Rates of Quadrupolar Aqueous Ions from Classical Molecular Dynamics Using Force-Field Specific Sternheimer Factors

The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is governed by the electric field gradient (EFG) fluctuations at their position. In classical molecular dynamics (MD), the electron cloud contribution to the EFG can be included via the Sternheimer approximation, in which the full EFG at the nucleus that can be computed using quantum density functional theory (DFT) is considered to be proportional to that arising from the external, classical charge distribution. In this work, we systematically assess the quality of the Sternheimer approximation as well as the impact of the classical force field (FF) on the NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In particular, we compare the rates obtained using an ab initio parametrized polarizable FF, a recently developed empirical FF with scaled ionic charges and a simple empirical nonpolarizable FF with formal ionic charges. Surprisingly, all three FFs considered yield good values for the rates of smaller and less polarizable solutes (Li⁺, Na⁺, K⁺, Cl^-), provided that a model-specific Sternheimer parametrization is employed. Yet, the polarizable and scaled charge FFs yield better estimates for divalent and more polarizable species (Mg²⁺, Ca²⁺, Cs⁺). We find that a linear relationship between the quantum and classical EFGs holds well in all of the cases considered; however, such an approximation often leads to quite large errors in the resulting EFG variance, which is directly proportional to the computed rate. We attempted to reduce the errors by including first order nonlinear corrections to the EFG, yet no clear improvement for the resulting variance has been found. The latter result indicates that more refined methods for determining the EFG at the ion position, in particular those that take into account the instantaneous atomic environment around an ion, might be necessary to systematically improve the NMR relaxation rate estimates in classical MD.

Nuclear magnetic resonance spin-lattice relaxation of lithium ions in aqueous solution by NMR and molecular dynamics

We study the aqueous solvation dynamics of lithium ions using nuclear magnetic resonance spectroscopy, molecular dynamics, and viscosity measurements. Several relaxation mechanisms are examined to explain the strong increases of spin-lattice relaxation toward high concentrations. The use of both ⁶Li and ⁷Li isotopes is helpful to identify the quadrupolar contribution to the relaxation rate. In particular, it is found that the quadrupolar interaction constitutes the strongest contribution above a concentration of ∼10 molal. The next-strongest contribution arises from interactions that scale with the square of the gyromagnetic ratio (mostly the dipolar interaction), and the experimental relaxation rates appear to be fully accounted for when these mechanisms are combined over the concentration range up to the saturation concentration. The study of solvation dynamics, particularly at high concentrations, could be of relevance for electrolyte dynamics in aqueous Li-ion rechargeable batteries.

Quadrupolar NMR Relaxation of Aqueous 127I-, 131Xe, and 133Cs+: A First-Principles Approach from Dynamics to Properties

Quadrupolar NMR relaxation rates were computed for aqueous ¹³³Cs⁺, ¹³¹Xe, and ¹²⁷I^- via Kohn-Sham (KS) density functional theory-based ab initio molecular dynamics and KS calculations of the electric field gradient (EFG) tensors along the trajectories. The resulting rates are within a factor of 1-3 of the experimental values and can be compared to available results from classical dynamics and EFGs from electrostatic models with corrections via Sternheimer antishielding factors. Relativistic effects are shown to have an enhancing effect on the magnitude of the EFGs. An analysis of the EFGs was carried out in terms of localized molecular orbitals to elucidate contributions from the solvent versus solute polarization and assess the validity of the Sternheimer approximation for these systems.

Molecular Dynamics Simulations of Ionic Liquids and Electrolytes Using Polarizable Force Fields

Many applications in chemistry, biology, and energy storage/conversion research rely on molecular simulations to provide fundamental insight into structural and transport properties of materials with high ionic concentrations. Whether the system is comprised entirely of ions, like ionic liquids, or is a mixture of a polar solvent with a salt, e.g., liquid electrolytes for battery applications, the presence of ions in these materials results in strong local electric fields polarizing solvent molecules and large ions. To predict properties of such systems from molecular simulations often requires either explicit or mean-field inclusion of the influence of polarization on electrostatic interactions. In this manuscript, we review the pros and cons of different treatments of polarization ranging from the mean-field approaches to the most popular explicit polarization models in molecular dynamics simulations of ionic materials. For each method, we discuss their advantages and disadvantages and emphasize key assumptions as well as their adjustable parameters. Strategies for the development of polarizable models are presented with a specific focus on extracting atomic polarizabilities. Finally, we compare simulations using polarizable and nonpolarizable models for several classes of ionic systems, discussing the underlying physics that each approach includes or ignores, implications for implementation and computational efficiency, and the accuracy of properties predicted by these methods compared to experiments.

Dielectric response in the vicinity of an ion: A nonlocal and nonlinear model of the dielectric properties of water

The goal of this work is to propose a simple continuous model that captures the dielectric properties of water at the nanometric scale. We write an electrostatic energy as a functional of the polarisation field containing a term in P⁴ and non-local Gaussian terms. Such a hamiltonian can reproduce two key properties of water: the saturation of the polarisation response of water in the presence of a strong electrostatic field and the nanometric dipolar correlations of the solvent molecules modifying the long range van der waals interaction. This model explores thus two fundamental aspects that have to be included in implicit models of electrolytes for a relevant description of electrostatic interactions at nanometric scales.

Quadrupolar 14N NMR Relaxation from Force-Field and Ab Initio Molecular Dynamics in Different Solvents

Quadrupolar NMR spin relaxation rates and corresponding line widths were computed for the quadrupolar nucleus ¹⁴N for neat acetonitrile as well as for 1-methyl-1,3-imidazole and 1-methyl-1,3,4-triazole in different solvents. Molecular dynamics (MD) was performed with forces from the Kohn-Sham (KS) theory (ab initio MD) and force-field molecular mechanics (classical MD), followed by KS electric field gradient (EFG) calculations. For acetonitrile the agreement of the ¹⁴N line width with experiment is very good. Relative line widths for the azole nitrogens are improved over simpler approximations used previously in conjunction with single-point calculations at the multiconfigurational self-consistent field level. Overall, the NMR line widths are computed within a factor of 2 of the experimental values, giving access to reasonable estimates both of the dynamic EFG variance in the solvated systems as well as the associated correlation times that determine the relaxation rates.

Quadrupolar NMR Relaxation from ab Initio Molecular Dynamics: Improved Sampling and Cluster Models versus Periodic Calculations

Quadrupolar NMR relaxation rates are computed for ¹⁷O and ²H nuclei of liquid water, and of ²³Na⁺, and ³⁵Cl^- in aqueous solution via Kohn-Sham (KS) density functional theory ab initio molecular dynamics (aiMD) and subsequent KS electric field gradient (EFG) calculations along the trajectories. The calculated relaxation rates are within about a factor of 2 of experimental results and improved over previous aiMD simulations. The relaxation rates are assessed with regard to the lengths of the simulations as well as configurational sampling. The latter is found to be the more limiting factor in obtaining good statistical sampling and is improved by averaging over many equivalent nuclei of a system or over several independent trajectories. Further, full periodic plane-wave basis calculations of the EFGs are compared with molecular-cluster atomic-orbital basis calculations. The two methods deliver comparable results with nonhybrid functionals. With the molecular-cluster approach, a larger variety of electronic structure methods is available. For chloride, the EFG computations benefit from using a hybrid KS functional.

Collective water dynamics in the first solvation shell drive the NMR relaxation of aqueous quadrupolar cations

Using molecular simulations, we analyze the microscopic processes driving the Nuclear Magnetic Resonance (NMR) relaxation of quadrupolar cations in water. The fluctuations of the Electric Field Gradient (EFG) experienced by alkaline and magnesium cations, which determine the NMR relaxation time, are mainly due to the dynamics of water molecules in their solvation shell. The dynamics of the ion plays a less important role, with the exception of the short-time dynamics in the lighter Li⁺ case, for which rattling in the solvent cage results in oscillations of the EFG autocorrelation function (ACF). Several microscopic mechanisms that may a priori contribute to the decay of the EFG-ACF occur in fact over too long time scales: entrance/exit of individual water molecules into/from the solvation shell, rotation of a molecule around the ion, or reorientation of the molecule. In contrast, the fluctuations of the ion-water distance are clearly correlated to that of the EFG. Nevertheless, it is not sufficient to consider a single molecule due to the cancellations arising from the symmetry of the solvation shell. The decay of the EFG-ACF, hence NMR relaxation, is in fact governed by the collective symmetry-breaking fluctuations of water in the first solvation shell.

Characterization of dimethylsulfoxide/glycerol mixtures: a binary solvent system for the study of “friction-dependent” chemical reactivity

The properties of binary mixtures of dimethylsulfoxide and glycerol, measured using several techniques, are reported.