An ab initio zeroth-order regular approximation (ZORA) theory for relativistic calculation of the nuclear magnetic shielding tensors is presented at the Hartree–Fock level. The nuclear magnetic shieldings tensors of hydrogen halides, HX (X=F, Cl, Br, and I), are calculated, and the results are compared to experimental values and other calculated results obtained using the Douglas–Kroll–Hess (DKH) transformation, the four-component random phase approximation (RPA), and the Dirac–Fock (DF) approaches. It is shown that the ZORA method underestimates the relativistic effects on the magnetic shieldings as compared to the four-component RPA results. However, as to the proton chemical shifts, the ZORA results are closer to the experimental proton shifts than those of the DKH and 4-RPA approaches.

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A Schrödinger-Pauli type two-component perturbation theory has been presented for the calculation of relativistic effects of nuclear magnetic shieldings. The expression for the relativistic nuclear magnetic shieldings are derived from the Douglas-Kroll transformation of the no-pair equation for a molecule, which bears a nuclear magnetic dipole moment, and which is placed in an external magnetic field. The exact form of the relativistic kinetic energy is included in the eigenvalue equation which is solved variationally. We calculated the relativistic mass correction effect on the nuclear magnetic shieldings in the four hydrogen halide molecules, HF, HCl, HBr, and HI, at the coupled Hartree-Fock (CHF) level. It was shown that the mass correction effect increases the nuclear magnetic shieldings of the halogen nuclei. The increments in the shieldings are proportional to about the third power of the atomic numbers of the halogen nuclei. This increase in the shieldings results from the mass correction effect concentrating the electrons in the vicinity of the heavy nucleus, the so-called relativistic contraction.

The results of hydrogen iodide in Table I were not correct and should be read as follows. The corrected results yield small negative values for the anisotropy of proton shielding of HI, which are consistent with previous reports. It is shown that the effects of the diamagnetic approximation are trivial in I shieldings.

Study of the importance of relativistic, correlation, and relaxation effects on ionization energy of atoms by a relativistic and correlated local density method A solution (Dirac electron in crossed, constant electric and magnetic fields) that has found a problem (relativistic quantized Hall effect) Am.The lowest order relativistic effect theory for nuclear magnetic shieldings was derived from a two-component positive energy Hamiltonian. It was shown that the previous relativistic shielding theory based on the two-component Hamiltonian is not gauge invariant and the new terms have to be added to make a result gauge invariant. The presented theory is gauge invariant to the order of (Z/137) 4 where Z is the atomic number of the heaviest atom in the molecule. One of the new contributions to the relativistic magnetic shieldings is a second-order perturbation term due to the combination of the spin-orbit interaction and the Fermi-contact interaction. A numerical estimation for this term was performed for the four hydrogen halides, HF, HCl, HBr, and HI. The computational results showed that the contribution of this term to the hydrogen shieldings is negligibly small, but the contribution to the halogen atoms is considerable.