Unravelling the effect of paramagnetic Ni²⁺ on the ¹³C NMR shift tensor for carbonate in Mg_2-xNi_xAl layered double hydroxides by quantum-chemical computations

Structural disorder and low crystallinity render it challenging to characterise the atomic-level structure of layered double hydroxides (LDH). We report a novel multi-step, first-principles computational workflow for the analysis of paramagnetic solid-state NMR of complex inorganic systems such as LDH, which are commonly used as catalysts and energy storage materials. A series of (CO32-)-C-13-labelled Mg2-xNixAl-LDH, x ranging from 0 (Mg2Al-LDH) to 2 (Ni2Al-LDH), features three distinct eigenvalues delta(11), delta(22) and delta(33) of the experimental C-13 chemical shift tensor. The delta(ii) correlate directly with the concentration of the paramagnetic Ni2+ and span a range of vertical bar delta(11) - delta(33)|vertical bar 0 ppm at x = 0, increasing to 950 ppm at x = 2. In contrast, the isotropic shift, delta(iso)(C-13), only varies by -14 ppm in the series. Detailed insight is obtained by computing (1) the orbital shielding by periodic density-functional theory involving interlayer water, (2) the long-range pseudocontact contribution of the randomly distributed Ni2+ ions in the cation layers (characterised by an ab initio susceptibility tensor) by a lattice sum, and (3) the close-range hyperfine terms using a full first-principles shielding machinery. A pseudohydrogen-terminated two-layer cluster model is used to compute (3), particularly the contact terms. Due to negative spin density contribution at the C-13 site arising from the close-by Ni2+ sites, this step is necessary to reach a semiquantitative agreement with experiment. These findings influence future NMR investigations of the formally closed-shell interlayer species within LDH, such as the anions or water. Furthermore, the workflow is applicable to a variety of complex materials.