Correlating Intermolecular Cross-Relaxation Rates with Distances and Coordination Numbers in Ionic Liquids

The HOESY NMR experiment is commonly used to probe ion associations in ionic liquids and their mixtures. The parameter measured in this experiment is the heteronuclear cross-relaxation rate σ, which has dimensions of s^-1. For intramolecular NOEs this scales as r^-6 where r is the internuclear distance, but in the intermolecular case (as typically probed in studies of ionic liquids), theory predicts a more complex behavior including a distance dependence that is affected by the relative frequencies of the nuclei involved. Specifically, for nuclei with similar resonance frequencies such as ¹H and ¹⁹F, it has been predicted that intermolecular NOEs will be sensitive to longer range distances than for nuclei with very different frequencies such as ¹H and ⁷Li. In this contribution, we test this theory using a combination of quantitative HOESY analysis and molecular dynamics simulations carried out on two different ionic liquid electrolyte systems. In agreement with theoretical predictions, we find excellent correlations between the experimentally measured ¹H-⁷Li NOEs and carbon-lithium distances below 4 Å, while longer distances (>6 Å) must be considered in order to obtain good correlations between ¹H-¹⁹F NOEs and carbon-fluorine coordination numbers. This demonstrates the utility of HOESY NMR in understanding structure and interactions in ionic liquids while also illustrating that care must be taken in interpreting the measured cross-relaxation rates.