Ab Initio Molecular Dynamics Study of Quadrupolar Spin Relaxation in an Ionic Liquid

This work implements a methodology for studying quadrupolar nuclear spin relaxation in ionic liquids. The dynamic behavior of the ions in the liquid is described by ab initio molecular dynamics (aiMD) with forces obtained from density functional theory (DFT) calculations with periodic boundary conditions and a non-hybrid functional. The electric field gradient (EFG) driving the quadrupolar relaxation was calculated with free boundary conditions, using clusters that contained the ion of interest surrounded by two coordination shells treated quantum mechanically and augmented with a solvation model. Tests showed that EFG calculations using only the first coordination shell, containing five nearest neighbors, also provide a suitable model, because the relaxation rates differ by no more than 4% from the results from the two-shell solvation. The results of this study show that the ${}^{2}H$ relaxation of the deuterated ethylammonium nitrate ( ${\text{EtND}}_3{\mathrm{NO}}_3$ ) occurs within the extreme narrowing regime for a spectrometer magnetic field $B_0=11.7$ T and is therefore characterized by the ensemble variance of the EFG and the correlation time associated with the EFG autocorrelation function. The quadrupolar relaxation of ${\text{EtND}}_3{\mathrm{NO}}_3$ demanded molecular dynamics production times longer than 330 ps and averaging over multiple ions, as well as independent trajectories to get suitably converged relaxation rates. The calculated ${}^{2}H$ relaxation rate is $1/T_1=13.3\pm 1.0$ Hz, about 60% above the rate reported experimentally. However, the approach utilized in the present study has an accuracy similar to, or better than, what has been previously reported for systems involving non-ionic solvents that required simulations of 100 ps duration or less.