² H Quadrupolar Coupling Constant: A Spectroscopic Ruler for Transition Metal–Hydride Bond Distances in Molecular and Surface Sites

Transition metal hydrides (TMHs) find numerous applications across fields from catalysis to H₂ storage. Yet, determining the structure of TMHs can remain a challenge, as hydrogen is difficult to detect by X-ray based or classical spectroscopic techniques. Considering that the deuterium isotope (D) is a quadrupolar nucleus (<i>I</i> = 1) and that a quadrupolar coupling constant (<i>C</i>_Q) depends on the distance between D and its bonding partner E (<i>d</i>_ED), we evaluate this trend across molecularly defined transition metal deuterides (TMDs) through a systematic investigation across TM block elements using both computations and experiments. We show that the M-D bond distance (<i>d</i>_MD) in [Å] correlates with the <i>C</i>_Q values in [kHz] as <i>d</i>_MD = 7.83(<i>C</i>_Q + 28.7)^-1/3─independently from the nature of the TM─with an accuracy >0.04-0.08 Å. Based on experimental <i>C</i>_Q values measured by ²H solid-state NMR, this simple correlation is then used to obtain the M-D bond distances in two silica-supported TMDs (M = Zr and Ir), notable heterogeneous catalysts representing early and late TMDs, where evaluating M-D bond distances by other means is very challenging. Considering the ease of measurement, this method is readily applicable to a large range of diamagnetic terminal M-Ds, from molecular to surface sites, making ²H NMR a method of choice to measure TMD bond distances.