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)][BF4], to provide a framework for future interpretation of NMR experiments. Our calculations demonstrate that the Sternheimer approximation holds for Na+ in [Im(21)][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 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, & lang;tau(EFG)& rang;, 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 similar to 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 & lang;tau(EFG)& rang;. Published under an exclusive license by AIP Publishing.