Localized orbital/local origin method for calculation and analysis of NMR shieldings. Applications to 13C shielding tensors

Abstract

A theory of NMR shielding tensors is derived from Ramsey’s expressions, using the framework of the random phase approximation (RPA) and localized molecular orbitals. By expanding angular momentum terms relative to a local origin for each orbital and using properties of the RPA solutions, we arrive at shielding expressions that contain no reference to an overall gauge origin and that lead to appropriate damping of basis set errors in contributions from distant groups. The expressions allow an analysis of the shielding into intrinsic bond and bond–bond coupling contributions. The resulting method is a variant of the coupled-Hartree–Fock approach. Ab initio results are presented for 13C isotropic shieldings and shielding tensors in a number of organic molecules ranging in size up to benzene. These results agree very well with experiment, for both isotropic shieldings and principal tensor components, even in double-zeta basis sets. For some low symmetry molecules we study the asymmetry of the shielding tensor and show that the antisymmetry can be quite large even if the anitsotropy is moderate. The bond analyses shed light on the effects of molecular structural features on the shieldings and their anisotropies, and emphasize in particular the conformational effects in bond–bond coupling contributions.