Relativistic DFT Calculations of Cadmium and Selenium Solid-State NMR Spectra of CdSe Nanocrystal Surfaces

Solid-state NMR spectra have been used to probe the structure of CdSe nanocrystals and propose detailed models of their surface structures. Density functional theory (DFT)-optimized cluster models that represent probable molecular structures of carboxylate-coordinated surface sites have been proposed. However, to the best of our knowledge, ¹¹³Cd and ⁷⁷Se chemical shifts have not been calculated for these surface models. We performed relativistic DFT calculations of cadmium and selenium magnetic shielding tensors on model compounds with previously measured solid-state NMR spectra with (i) the four-component Dirac-Kohn-Sham (DKS) Hamiltonian and (ii) the scalar and (iii) spin-orbit levels within the ZORA Hamiltonian. Molecular clusters with Cd and Se sites in varying bonding environments were used to model CdSe (100) and CdSe(111) surfaces capped with carboxylic acid ligands. Our calculations identify the observed ¹¹³Cd isotropic chemical shifts δ(iso) of -465, -318, and -146 ppm arising from CdSeO₃, CdSe₂O₂, and CdSe₃O surface groups, respectively, with very good agreement with experimental measurements. The ¹¹³Cd chemical shifts linearly decrease with the number of O-neighbors. The calculated spans (δ₁₁ - δ₃₃) encompass the experimental values for CdSe₃O and CdSe₂O₂ clusters but are slightly larger than the measured value for CdSeO₃ clusters. Relativistic DFT calculations predicted a one-bond ¹¹³Cd-⁷⁷Se scalar coupling of 258 Hz, which is in good agreement with the experimental values of 250 Hz. With a dense coverage of carboxylic acid ligands, the CdSe (100) surface shows a distribution of Cd-Se bond lengths and J-couplings. Relativistic DFT simulations thus aid in interpretation of NMR spectra of CdSe nanocrystals and related nanomaterials.