  Nuclear magnetic resonance relaxometry represents a powerful tool for
extracting dynamic information. Yet, obtaining links to molecular motion is
challenging for many ions that relax through the quadrupolar mechanism, which
is mediated by electric field gradient fluctuations and lacks a detailed
microscopic description. For sodium ions in aqueous electrolytes, we combine ab
initio calculations to account for electron cloud effects with classical
molecular dynamics to sample long-time fluctuations, and obtain relaxation
rates in good agreement with experiments over broad concentration and
temperature ranges. We demonstrate that quadrupolar nuclear relaxation is
sensitive to subpicosecond dynamics not captured by previous models based on
water reorientation or cluster rotation. While ions affect the overall water
retardation, experimental trends are mainly explained by dynamics in the first
two solvation shells of sodium, which contain mostly water. This work thus
paves the way to the quantitative understanding of quadrupolar relaxation in
electrolyte and bioelectrolyte systems.
