Second- and third-order spin-orbit contributions to nuclear shielding tensors

Abstract

We present analytical calculations of the electronic spin–orbit interaction contribution to nuclear magnetic shielding tensors using linear and quadratic response theory. The effects of the Fermi contact and the spin-dipole interactions with both the one- and two-electron spin–orbit Hamiltonians, included as first-order perturbations, are studied for the H2X (X=O, S, Se, and Te), HX (X=F, Cl, Br, and I), and CH3X (X=F, Cl, Br, and I) systems using nonrelativistic multiconfiguration self-consistent field reference states. We also present the first correlated study of the spin–orbit-induced contributions to shielding tensors arising from the magnetic field dependence of the spin–orbit Hamiltonian. While the terms usually considered are formally calculated using third-order perturbation theory, the magnetic-field dependent spin-orbit Hamiltonian requires a second-order calculation only. For the hydrogen chalcogenides, we show that contributions often neglected in studies of spin–orbit effects on nuclear shieldings, the spin-dipole coupling mechanism and the coupling of the two-electron spin–orbit Hamiltonian to the Fermi-contact operator, are important for the spin–orbit effect on the heavy-atom shielding, adding up to about half the value of the one-electron spin–orbit interaction with the Fermi-contact contribution. Whereas the second-order spin-orbit-induced shieldings of light ligands are small, the effect is larger for the heavy nuclei themselves and of opposite sign compared to the third-order contribution.