Molecular dynamic simulation of quadrupole relaxation of atomic ions in aqueous solution

Characterization of the Coordination and Solvation Dynamics of Solvated Systems─Implications for the Analysis of Molecular Interactions in Solutions and Pure H2O

The characterization of solvation shells of atoms, ions, and molecules in solution is essential to relate solvation properties to chemical phenomena such as complex formation and reactivity. Different definitions of the first-shell coordination sphere from simulation data can lead to potentially conflicting data on the structural properties and associated ligand exchange dynamics. The definition of a solvation shell is typically based on a given threshold distance determined from the respective solute-solvent pair distribution function g(r) (i.e., GC). Alternatively, a nearest neighbor (NN) assignment based on geometric properties of the coordination complex without the need for a predetermined cutoff criterion, such as the relative angular distance (RAD) or the modified Voronoi (MV) tessellation, can be applied. In this study, the effect of different NN algorithms on the coordination number and ligand exchange dynamics evaluated for a series of monatomic ions in aqueous solution, carbon dioxide in aqueous and dichloromethane solutions, and pure liquid water has been investigated. In the case of the monatomic ions, the RAD approach is superior in achieving a well separated definition of the first solvation layer. In contrast, the MV algorithm provides a better separation of the NNs from a molecular point of view, leading to better results in the case of solvated CO2. When analyzing the coordination environment in pure water, the cutoff-based GC framework was found to be the most reliable approach. By comparison of the number of ligand exchange reactions and the associated mean ligand residence times (MRTs) with the properties of the coordination number autocorrelation functions, it is shown that although the average coordination numbers are sensitive to the different definitions of the first solvation shell, highly consistent estimates for the associated MRT of the solvated system are obtained in the majority of cases.

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⟩.

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.

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.

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.

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

Nuclear Magnetic Resonance (NMR) relaxation is sensitive to the local structure and dynamics around the probed nuclei. The Electric Field Gradient (EFG) is the key microscopic quantity to understand the NMR relaxation of quadrupolar ions, such as (7)Li(+), (23)Na(+), (25)Mg(2+), (35)Cl(-), (39)K(+), or (133)Cs(+). Using molecular dynamics simulations, we investigate the statistical and dynamical properties of the EFG experienced by alkaline, alkaline Earth, and chloride ions at infinite dilution in water. Specifically, we analyze the effect of the ionic charge and size on the distribution of the EFG tensor and on the multi-step decay of its auto-correlation function. The main contribution to the NMR relaxation time arises from the slowest mode, with a characteristic time on the picosecond time scale. The first solvation shell of the ion plays a dominant role in the fluctuations of the EFG, all the more that the ion radius is small and its charge is large. We propose an analysis based on a simplified charge distribution around the ion, which demonstrates that the auto-correlation of the EFG, hence the NMR relaxation time, reflects primarily the collective translational motion of water molecules in the first solvation shell of the cations. Our findings provide a microscopic route to the quantitative interpretation of NMR relaxation measurements and open the way to the design of improved analytical theories for NMR relaxation for small ionic solutes, which should focus on water density fluctuations around the ion.

Computing the 7Li NMR chemical shielding of hydrated Li+ using cluster calculations and time-averaged configurations from ab initio molecular dynamics simulations

Ab initio molecular dynamics (AIMD) simulations have been used to predict the time-averaged Li NMR chemical shielding for a Li(+) solution. These results are compared to NMR shielding calculations on smaller Li(+)(H(2)O)(n) clusters optimized in either the gas phase or with a polarizable continuum model (PCM) solvent. The trends introduced by the PCM solvent are described and compared to the time-averaged chemical shielding observed in the AIMD simulations where large explicit water clusters hydrating the Li(+) are employed. Different inner- and outer-coordination sphere contributions to the Li NMR shielding are evaluated and discussed. It is demonstrated an implicit PCM solvent is not sufficient to correctly model the Li shielding, and that explicit inner hydration sphere waters are required during the NMR calculations. It is also shown that for hydrated Li(+), the time averaged chemical shielding cannot be simply described by the population-weighted average of coordination environments containing different number of waters.

Sodium ion distribution in the vitreous body

We have studied the nuclear magnetic resonance (NMR) relaxation behavior, and thus the dynamic properties, of the sodium ion in the vitreous body at different temperatures. The 23Na NMR spectrum exhibits a resonance, the intensity of which accounts for an ion visibility of 100%. The 23Na longitudinal and transverse relaxation times, at all temperatures but the highest, present two components, suggesting that the sodium ions are present in two states of different mobility, whose populations are in slow exchange on the NMR time scale. The correlation times and quadrupole coupling constants for the two sodium pools have been derived. The faster relaxation of a fraction of the vitreal sodium has tentatively been ascribed to the influence of the macromolecular framework of the vitreous body. The reported information may be of use for the understanding of the diagnostic applications of 23Na magnetic resonance imaging of the ocular structures.

87Rb+ spin relaxation in enzymically purified and in untreated iota-carrageenan

The temperature dependences of the transverse (R2) and longitudinal (R1) n.m.r. relaxation rates of 87Rb+ in aqueous 5% iota-carrageenan have been compared with similar data for a sample purified by treatment with kappa-carrageenase. In each sample, the relaxation rates were sensitive to the conformation (helix or random coil). In the intact sample, the small (less than or equal to 5%) fraction of kappa-carrageenan (which, in its helical state, specifically binds rubidium ions) was solely responsible for the pronounced line-broadening that has been observed hitherto for 87Rb in iota-carrageenan gels. In the purified sample, the effects on the relaxation of 87Rb induced by iota-carrageenan are similar to those found in comparable systems in the absence of site-binding of the ions. Thus, there was a modest enhancement of the relaxation with R1 approximately R2 for the flexible coil conformation and a comparably larger effect, with significant contributions from dynamic processes on the time-scale of the inverse resonance frequency or longer, for the thicker, more highly charged and rigid helix conformation of iota-carrageenan.