Water-separated ion pairs cause the slow dielectric mode of magnesium sulfate solutions

We compare the dielectric spectra of aqueous MgSO₄ and Na₂SO₄ solutions calculated from classical molecular dynamics simulations with experimental data, using an optimized thermodynamically consistent sulfate force field. Both the concentration-dependent shift of the static dielectric constant and the spectral shape match the experimental results very well for Na₂SO₄ solutions. For MgSO₄ solutions, the simulations qualitatively reproduce the experimental observation of a slow mode, the origin of which we trace back to the ion-pair relaxation contribution via spectral decomposition. The radial distribution functions show that Mg²⁺ and SO42- ions form extensive water-separated - and thus strongly dipolar - ion pairs, the orientational relaxation of which provides a simple physical explanation for the prominent slow dielectric mode in MgSO₄ solutions. Remarkably, the Mg²⁺-SO42- ion-pair relaxation extends all the way into the THz range, which we rationalize by the vibrational relaxation of tightly bound water-separated ion pairs. Thus, the relaxation of divalent ion pairs can give rise to widely separated orientational and vibrational spectroscopic features.