A DFT/ZORA Study of Cadmium Magnetic Shielding Tensors: Analysis of Relativistic Effects and Electronic-State Approximations

Theoretical considerations are discussed for the accurate prediction of cadmium magnetic shielding tensors using relativistic density functional theory (DFT). Comparison is made between calculations that model the extended lattice of the cadmium-containing solids using periodic boundary conditions and pseudopotentials with calculations that use clusters of atoms. The all-electron cluster-based calculations afford an opportunity to examine the importance of (i) relativistic effects on cadmium magnetic shielding tensors, as introduced through the ZORA Hamiltonian at either the scalar (SC) or spin–orbit (SO) levels and (ii) variation in the class of the DFT approximation. Twenty-three combinations of pseudopotentials or all-electron methods, DFT functionals, and relativistic treatments are assessed for the prediction of the principal components of the magnetic shielding tensors of 30 cadmium sites. We find that the inclusion of SO coupling can increase the cadmium magnetic shielding by as much as ca. 1100 ppm for a certain principal values; these effects are most pronounced for cadmium sites featuring bonds to other heavy atoms such as cadmium, iodine, or selenium. The best agreement with experimental values is found at the ZORA SO level in combination with a hybrid DFT method featuring a large admixture of Hartree–Fock exchange such as BH&HLYP. Finally, a theoretical examination is presented of the magnetic shielding tensor of the Cd­(I) site in Cd2(AlCl4)2.