Solid-state NMR and density functional investigation of carbon-13 shielding tensors in metal-olefin complexes

We have determined the principal elements of the chemical shift tensors for a series of metal-olefin complexes: [Ag(cod)₂]BF₄ (cod = cis,cis-cycloocta-1,5-diene), [CuCl(cod)]₂, PtCl₂(cod), [RhCl(cod)]₂, and K[PtCl₃(C₂H₄)] using magic-angle sample spinning and a Bayesian probability method to deduce μ, ρ in the Herzfeld-Berger equations. These principal elements have also been computed by using density functional methods with two different types of functionals and partial geometry optimization. The overall slope and R² values between the theoretical and experimental tensor elements are good, ranging from 1.06 to 1.16 for the slope (versus the ideal value of 1) and 0.98-0.99 for the goodness of fit parameter R² (versus the ideal value of 1). The use of a hybrid functional results in a slightly worse slope, an effect which is largest for the compounds with the largest paramagnetic shifts. There are no particularly good correlations between C-C bond lengths, isotropic/anisotropic shift tensor elements or computed bond orders; however, the correlation between shielding and (Mulliken) charge of ∼ -120 ppm/electron is consistent with previous experimental estimates on olefins and aromatic compounds. The orientations of the shielding tensor elements in the cod complexes change in a relatively continuous manner with increases in shielding (from d¹⁰ to d⁸ metals), with δ₃₃ becoming rotated (37.5°) from the normal to the C=C bond axis in [RhCl(cod)]₂. Overall, these results indicate that density functional methods permit the relatively accurate reproduction of metal-ligand shielding patterns in systems whose structures are known, which should facilitate their use in probing metal-ligand geometries in systems whose structures are less certain, such as in metalloproteins.