Transition-metal hydrides (TMHs) find numerous applications across fields, from catalysts to H₂ storage. Yet, determining the structure of TMHs remains a challenge in many instances, as hydrogen is a light element difficult to detect by X-ray based techniques and M-H bonds mostly display a low dipole moment, hence difficult to observe by IR. In addition, the NMR chemical of metal hydrides is dominated by spin orbit coupling contribution, making it difficult to chemically interpret this information. Considering that the deuterium isotope (D) is a quadrupolar nucleus (I=1) and that the associated quadrupolar coupling constant (C_Q) should depend on the distance between D and its bonding partner M (d_MD), we evaluate this trend across molecularly-defined transition-metal deuterides (TMDs) through a systematic investigation across the TM block using both computations and experiments. In this work,¹ we show that the M–D bond distance (d_MD) in [Å] correlates with the C_Q values in [kHz] as d_MD= 7.83(C_Q + 28.7)^-1/3, with an accuracy exceeding 0.04-0.08 Å.

Based on experimental C_Q values measured by solid-state ²H NMR, this simple correlation can be used to measure M-D bond distances, illustrated in this work for two silica-supported MDs (M = Zr and Ir), notable heterogeneous catalysts representing early and late TMDs, for which alternative approaches are extremely challenging due to the low metal loadings. Considering the ease of measurement, this method is readily applicable to a large range of diamagnetic terminal MDs (η< 0.1),² from molecular to surface sites, making ²H NMR a method of choice to measure bond distances in TMDs, using the experimental C_Q as a 'spectroscopic ruler'.

[1] Domenico Gioffrè, et. al, J. Am. Chem. Soc. 2025, 147, 15936−15941

[2] Scott  R. Docherty, Philipp Schärtz, Domenico Gioffrè, et. al, Helv. Chim. Acta 2024, 107, e202300173