Nuclear MagneticResonance and Computational Studiesof Sodium Ions in an Ionic Liquid/Water Mixture

We report a computational protocol for simulating electric field gradient dynamics around Na⁺ cations in mixtures of 1-ethyl-3-methylimidazolium tetrafluoroborate ([Im₂₁][BF₄]) and water validated by comparison to measurements of nuclear magnetic resonance (NMR) <i>T</i>₁ relaxation times. Our protocol combines classical molecular dynamics simulations of a scaled charge model of [Im₂₁][BF₄] and TIP4Pew water to generate the electric field gradient (EFG) correlation function, <i>C</i>_EFG(<i>t</i>), with quantum chemical calculations for determining the EFG variance ⟨Vzz2⟩. Although we demonstrate that the Sternheimer approximation is as valid in these mixtures as it is in neat water, we do not recommend using the Sternheimer approximation as it underestimates ⟨Vzz2⟩ by ∼10% compared to a set of computationally efficient density functional theory calculations. Our protocol is capable of reproducing both the composition- and temperature-dependence of <i>T</i>₁ over the full range of experimentally accessible [Im₂₁][BF₄]/water compositions and a temperature range of 285–350 K. We also show that scaling the [Im₂₁][BF₄] charges does not simply speed up the dynamics of the solvent, but has effects on the shape of <i>C</i>_EFG(<i>t</i>). Following validation of our protocol, we analyze the shape and relaxation times of <i>C</i>_EFG(<i>t</i>) to show that the mechanism by with <i>T</i>₁ changes is different when the composition of the mixture varies compared to changes in temperature. As composition changes, the balance between inertial and diffusive relaxation alters, whereas temperature only affects the time scale of the diffusion portion of the relaxation. We also show that solvation shell of Na⁺ in these mixtures is significantly more labile than in neat [Im₂₁][BF₄] and that water and BF₄^– anions compete to be in the Na⁺ solvation shell. This validated computational protocol opens the door to more detailed interpretation of NMR <i>T</i>₁ relaxation experiments of monatomic ions in complex liquid environments.