Calculation of nuclear magnetic shieldings. XII. Relativistic no-pair equation

Abstract

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.