NMR Crystallography: Evaluation of Hydrogen Positions in Hydromagnesite by ¹³ C{ ¹ H} REDOR Solid-State NMR and Density Functional Theory Calculation of Chemical Shielding Tensors

Solid-state NMR measurements coupled with density functional theory (DFT) calculations demonstrate how hydrogen positions can be refined in a crystalline system. The precision afforded by rotational-echo double-resonance (REDOR) NMR to interrogate ¹³ C– ¹ H distances is exploited along with DFT determinations of the ¹³ C tensor of carbonates (CO ₃ ²⁻ ). Nearby ¹ H nuclei perturb the axial symmetry of the carbonate sites in the hydrated carbonate mineral, hydromagnesite [4 MgCO ₃ ⋅Mg(OH) ₂ ⋅4 H ₂ O]. A match between the calculated structure and solid-state NMR was found by testing multiple semi-local and dispersion-corrected DFT functionals and applying them to optimize atom positions, starting from X-ray diffraction (XRD)-determined atomic coordinates. This was validated by comparing calculated to experimental ¹³ C{ ¹ H} REDOR and ¹³ C chemical shift anisotropy (CSA) tensor values. The results show that the combination of solid-state NMR, XRD, and DFT can improve structure refinement for hydrated materials.