  The nuclear magnetic resonance (NMR) relaxation of quadrupolar nuclei is
governed by the electric field gradient (EFG) fluctuations at their position.
In classical molecular dynamics (MD), the electron cloud contribution to the
EFG can be included via the Sternheimer approximation, in which the full EFG at
the nucleus that can be computed using quantum DFT is considered to be
proportional to that arising from the external, classical charge distribution.
In this work, we systematically assess the quality of the Sternheimer
approximation as well as the impact of the classical force field (FF) on the
NMR relaxation rates of aqueous quadrupolar ions at infinite dilution. In
particular, we compare the rates obtained using an ab initio parametrized
polarizable FF, a recently developed empirical FF with scaled ionic charges and
a simple empirical non-polarizable FF with formal ionic charges. Surprisingly,
all three FFs considered yield good values for the rates of smaller and less
polarizable solutes, provided that a model-specific Sternheimer parametrization
is employed. Yet, the polarizable and scaled charge FFs yield better estimates
for divalent and more polarizable species. We find that a linear relationship
between the quantum and classical EFGs holds well in all of the cases
considered, however, such an approximation often leads to quite large errors in
the resulting EFG variance, which is directly proportional to the computed
rate. We attempted to reduce the errors by including first order nonlinear
corrections to the EFG, yet no clear improvement for the resulting variance has
been found. The latter result indicates that more refined methods for
determining the EFG at the ion position, in particular those that take into
account the instantaneous atomic environment around an ion, might be necessary
to systematically improve the NMR relaxation rate estimates in classical MD.
