NMR relaxation rates of quadrupolar aqueous ions from classical molecular dynamics using force-field specific Sternheimer factors

TL;DR

This study evaluates the accuracy of the Sternheimer approximation in classical MD simulations for predicting NMR relaxation rates of quadrupolar ions in water, highlighting the influence of force field choice and the need for refined EFG calculation methods.

Contribution

It systematically assesses the impact of different force fields and the Sternheimer approximation on NMR relaxation rate predictions for aqueous ions, revealing limitations and potential improvements.

Findings

All force fields gave good rates for small, less polarizable ions with model-specific Sternheimer parameters.

Polarizable and scaled charge force fields better estimate rates for divalent, more polarizable ions.

Including nonlinear corrections to EFG did not significantly improve variance estimates.

Abstract

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.