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-methylimidizolium 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, CEFG( 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 decorrelation attributable to inertial solvent motion and the remainder to a highly distributed diffusional processes. Integral relaxation times, <τEFG>, 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]- are 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 <τEFG>.