Quasirelativistic theory for the magnetic shielding constant. I. Formulation of Douglas–Kroll–Hess transformation for the magnetic field and its application to atomic systems

Abstract

A two-component quasirelativistic theory based on the Douglas–Kroll–Hess (DKH) transformation has been developed to study magnetic properties of molecules. The proposed Hamiltonian includes the relativistic magnetic vector potential in the framework of the DKH theory, and is applicable to the calculations of magnetic properties without further expansion in powers of c−1. By combining with the finite-perturbation theory and the generalized-UHF method, new pictures of the magnetic shielding constant are derived. We apply the theory to calculations of the magnetic shielding constants of He isoelectronic systems, Ne isoelectronic systems, and noble gas atoms. The results of the present theory compare well with those of the four-component Dirac–Hartree–Fock calculations; the differences were within 3%. We note that the quasirelativistic theory that handles the magnetic vector potential at a nonrelativistic level greatly underestimates the relativistic effect. The so-called “picture change” effect is quite important for the magnetic shielding constant of heavy elements. The change in the orbital picture plays a significant role in the valence-orbital magnetic response as well as the core-orbital one. The effect of the finite nucleus is also studied using Gaussian nucleus model. The present theory reproduces the correct behavior of the finite-nucleus effect that has been reported with the Dirac theory. In contrast, the nonrelativistic theory and the quasirelativistic theory with the nonrelativistic vector potential underestimate the finite-nucleus effect.