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

Abstract

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>.

Electrical noise in electrolytes: a theoretical perspective

“…56,58 Quadrupolar relaxation in ionic liquids has also recently been investigated using molecular simulations. 57 The relevant autocorrelation function hV zz (t)V zz (0)i can be related to the charge-charge intermediate scattering function F qq ( k,t) of the electrolyte, see eqn (6). As shown by Perng and Ladanyi, 133 hV zz ðtÞV zz ð0Þiz…”

“…56,58 Quadrupolar relaxation in ionic liquids has also recently been investigated using molecular simulations. 57…”

“…47 Here again, molecular simulations prove very useful to quantitatively model the EFG fluctuations and open the way to the interpretation of quadrupolar NMR relaxation in terms of molecular motion. 48–58…”

“…47 Here again, molecular simulations prove very useful to quantitatively model the EFG uctuations and open the way to the interpretation of quadrupolar NMR relaxation in terms of molecular motion. [48][49][50][51][52][53][54][55][56][57][58] The dynamics of charge uctuations are also related to the static correlations between ions, as well as with the polar solvent. These correlations are generally understood in terms of screening: of the electrostatic interactions between ions by the solvent (with the reduction of the Coulomb interaction by the permittivity of the latter) and of the electrostatic potential by the ions (with the canonical Debye-Hückel theory and corresponding screening length).…”

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

“…An even simpler embedding strategy specific to EFG calculations relies on the empirical Sternheimer approximation, which assumes a linear relationship between the external electric field acting on the embedded species and the EFG. The Sternheimer approximation is computationally advantageous and has been used effectively in simulations of EFG dynamics, − but its usefulness is limited due to the dependence of the empirical coefficients used in relation on the specific system and its geometry. − Additionally, its validity in the condensed phase has been questioned, and the addition of higher-order terms in the electronic response has been proposed. , The need for explicit quantum mechanical treatment of the electrons in the molecule is thus commonly recognized in the community; therefore, several non-embedding quantum mechanical approaches have been used by various researchers. One method models only the nearest atoms in the system and neglects the environment completely, another targets only the shift in the largest diagonal component of the EFG relative to a reference calculation, and other approaches are based on the error compensation ansatz. , In this work, we turn to the explicit quantum-mechanical treatment of the embedded species and embedding methods based on frozen-density embedding theory (FDET), in which the embedding potential (multiplicative embedding operator) is given as a sum of the classical electrostatic component and the nonclassical part representing the quantum confinement by means of a universal bifunctional. − …”