Solid-state 185/187Re NMR and GIPAW DFT study of perrhenates and Re2(CO)10: chemical shift anisotropy, NMR crystallography, and a metal–metal bond

Abstract

Advances in solid-state nuclear magnetic resonance (SSNMR) methods, such as dynamic nuclear polarization (DNP), intricate pulse sequences, and increased applied magnetic fields, allow for the study of systems which even very recently would be impractical. However, SSNMR methods using certain quadrupolar probe nuclei (i.e., I > 1/2), such as ^185/187Re remain far from fully developed due to the exceedingly strong interaction between the quadrupole moment of these nuclei and local electric field gradients (EFGs). We present a detailed high-field (B₀ = 21.1 T) experimental SSNMR study on several perrhenates (KReO₄, AgReO₄, Ca(ReO₄)₂·2H₂O), as well as ReO₃ and Re₂(CO)₁₀. We propose solid ReO₃ as a new rhenium SSNMR chemical shift standard due to its reproducible and sharp ^185/187Re NMR resonances. We show that for KReO₄, previously poorly understood high-order quadrupole-induced effects (HOQIE) on the satellite transitions can be used to measure the EFG tensor asymmetry (i.e., η_Q) to nearly an order-of-magnitude greater precision than competing SSNMR and nuclear quadrupole resonance (NQR) approaches. Samples of AgReO₄ and Ca(ReO₄)₂·2H₂O enable us to comment on the effects of counter-ions and hydration upon Re(VII) chemical shifts. Calcium-43 and ^185/187Re NMR tensor parameters allow us to conclude that two proposed crystal structures for Ca(ReO₄)₂·2H₂O, which would be considered as distinct, are in fact the same structure. Study of Re₂(CO)₁₀ provides insights into the effects of Re–Re bonding on the rhenium NMR tensor parameters and rhenium oxidation state on the Re chemical shift value. As overtone NQR experiments allowed us to precisely measure the ^185/187Re EFG tensor of Re₂(CO)₁₀, we were able to measure rhenium chemical shift anisotropy (CSA) for the first time in a powdered sample. Experimental observations are supported by gauge-including projector augmented-wave (GIPAW) density functional theory (DFT) calculations, with NMR tensor calculations also provided for NH₄ReO₄, NaReO₄ and RbReO₄. These calculations are able to reproduce many of the experimental trends in rhenium δ_iso values and EFG tensor magnitudes. Using KReO₄ as a prototypical perrhenate-containing system, we establish a correlation between the tetrahedral shear strain parameter (|ψ|) and the nuclear electric quadrupolar coupling constant (C_Q), which enables the refinement of the structure of ND₄ReO₄. Shortcomings in traditional DFT approaches, even when including relativistic effects via the zeroth-order regular approximation (ZORA), for calculating rhenium NMR tensor parameters are identified for Re₂(CO)₁₀.