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

We present analytical calculations of the electronic spin-orbit interaction contribution to nuclear magnetic shielding tensors using linear and quadra tic response theory. The effects of the Fermi contact and the spin-dipole i nteractions with both the one- and two-electron spin-orbit Hamiltonians, in cluded as first-order perturbations, are studied for the H2X (X=O, S, Se, a nd Te), HX (X=F, Cl, Br, and I), and CH3X (X=F, Cl, Br, and I) systems usin g nonrelativistic multiconfiguration self-consistent field reference states . We also present the first correlated study of the spin-orbit-induced cont ributions to shielding tensors arising from the magnetic field dependence o f the spin-orbit Hamiltonian. While the terms usually considered are formal ly calculated using third-order perturbation theory, the magnetic-field dep endent 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 coupli ng 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-electro n spin-orbit interaction with the Fermi-contact contribution. Whereas the s econd-order spin-orbit-induced shieldings of light ligands are small, the e ffect is larger for the heavy nuclei themselves and of opposite sign compar ed to the third-order contribution. (C) 1999 American Institute of Physics. [S0021-9606(99)30731-5].