Abstract

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 ₁₃CO₃²⁻-labelled Mg_2−xNi_xAl-LDH, x ranging from 0 (Mg₂Al-LDH) to 2 (Ni₂Al-LDH), features three distinct eigenvalues δ₁₁, δ₂₂ and δ₃₃ of the experimental ₁₃C chemical shift tensor. The δ_ii correlate directly with the concentration of the paramagnetic Ni²⁺ and span a range of |δ₁₁ − δ₃₃| ≈ 90 ppm at x = 0, increasing to 950 ppm at x = 2. In contrast, the isotropic shift, δ_iso(¹³C), 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 ¹³C 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.