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

Assessment of Approximations to the Embedding Potential in Frozen-Density Embedding Theory for the Calculation of Electric Field Gradients

The approximations to the embedding potential in frozen-density embedding theory (FDET) have been assessed for the first time for the calculation of the electric field gradient (EFG) at a nucleus. FDET-based methods using a hierarchy of approximations are applied to evaluate the EFG at the nuclei of an HCl molecule in several noncovalently bound clusters chosen to represent potential liquid or molecular crystal systems. A detailed assessment of such approximations is made for the Hartree-Fock treatment of electron-electron correlation (both in FDET and in the reference calculations for the whole cluster). The emerging choice of the optimal set of approximations is reconfirmed in calculations in which electron-electron calculations are treated at the MP2 level. Our optimized protocol produces average errors in the complexation-induced EFG shift on the order of 25% relative to conventional quantum mechanical calculations for the whole cluster. This protocol is shown to be numerically robust and leads to enormous computational savings compared to a complete quantum mechanical treatment of the embedded species and its environment. For a cluster comprising a Na+ cation and up to 24 water molecules, the computation time is reduced by a factor of 30,000 at the expense of introducing an error in the environment-induced EFG shift of 22%.

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.

Assessing the Validity of NMR Relaxation Rates Obtained from Coarse-Grained Simulations of PEG-Water Mixtures

NMR relaxometry is a powerful and well-established experimental approach for characterizing dynamic processes in soft matter systems. All-atom (AA) resolved simulations are typically employed to gain further microscopic insights while reproducing the relaxation rates R₁. However, such approaches are limited to time and length scales that prevent to model systems such as long polymer chains or hydrogels. Coarse graining (CG) can overcome this barrier at the cost of losing atomistic details that impede the calculation of NMR relaxation rates. Here, we address this issue by performing a systematic characterization of dipolar relaxation rates R₁ on a PEG-H₂O mixture at two different levels of details: AA and CG. Remarkably, we show that NMR relaxation rates R₁ obtained at the CG level obey the same trends when compared to AA calculations but with a systematic offset. This offset is due to, on the one hand, the lack of an intramonomer component and, on the other hand, the inexact positioning of the spin carriers. We show that the offset can be corrected for quantitatively by reconstructing a posteriori the atomistic details for the CG trajectories.

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⟩.