  Mode-coupling theory provides a unified description of the rotational and
translational dynamics of polyatomic ions. These molecular ions are distinct
from usual models of ion diffusion, such as K+ , Cl- etc., and also different
from rotational dynamics of dipolar molecules often modeled in dielectric
continuum models as point dipoles. Both these approaches are untenable for
polyatomic ions. Here rotational and translational dynamics are so strongly
coupled that one obtains a more coherent description by treating them together.
We carry out theoretical and computational studies of a series of well-known
polyatomic ions, namely sulfate, nitrate and acetate ions. All the three ions
exhibit different rotational diffusivity, with that of nitrate ion being
considerably larger than the other two. They all defy the hydrodynamic laws of
size dependence. Study of the local structure around the ions provides valuable
insight into the origin of these differences. We carry out a detailed study of
the rotational diffusion of these ions by extensive computer simulation and
using the theoretical approaches of the dielectric friction developed by
Fatuzzo-Mason (FM) and Nee-Zwanzig (NZ), and subsequently generalized by Alavi
and Waldeck. We develop a self-consistent mode-coupling theory (SC-MCT)
formalism that helps elucidating the role of coupling between translational and
rotational motion of these ions. In fact, these two motions self-consistently
determine the value of each other. The RISM-based MCT suggests an interesting
relation between the torque-torque and the force-force time correlation
function with the proportionality constant being determined by the geometry and
the charge distribution of the polyatomic molecule.We point out several
parallelism between the theories of translational and rotation friction
calculations of ions in dipolar liquids.
