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

The T 1 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, [Im 21 ][BF 4 ], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na + in [Im 21 ][BF 4 ], 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 T 1 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 [BF 4 ] - anions and directly coordinated by ∼6 fluorine atoms. Exchange of [BF 4 ] - anions is rare on the 25-50 ns timescale and suggests that motion of solvent-shell [BF 4 ] - is the primary mechanism for the EFG fluctuations. Different couplings of [BF 4 ] - translational and rotational diffusion to viscosity are shown to be the source of the non-hydrodynamic scaling of ⟨τ EFG ⟩.