Calculation of NMR chemical shifts using relativistic wave functions

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A two-component relativistic SCF perturbation theory, based on the Douglas-Kroll-Hess (DKH) transformation, was applied to the calculation of nuclear magnetic shielding tensors of hydrogen halides, HX (X=F, Cl, Br, I). Calculations were performed via the unrestricted coupled Hartree-Fock (CHF) scheme using gauge-including atomic orbitals (GIAOs) at four different levels. At the level I calculation, both the scalar relativistic (SR) and spin-orbit (SO) interactions were included in the zeroth-order Hamiltonian. However, the magnetic perturbation Hamiltonians were treated nonrelativistically. The results of these calculations indicated a large interplay between the SR and SO interactions. The level I calculation was found to be insufficient to explain the full relativistic effect on the halogen atom shielding. In order to reproduce the full relativistic effect, the mass-velocity effect on the magnetic perturbation Hamiltonians was introduced at the level II to IV calculations. Inclusion of the mass-velocity effects into all of the perturbation Hamiltonians, made at levels III and IV, improved the results greatly. The cross term between the nuclear attraction potential and the magnetic vector potential was introduced approximately in level IV. The level III calculation agreed most closely with the four-component relativistic random phase approximation (RPA) calculation by Visscher et al.