Four-component relativistic theory for nuclear magnetic shielding constants: Critical assessments of different approaches

Abstract

Both formal and numerical analyses have been carried out on various exact and approximate variants of the four-component relativistic theory for nuclear magnetic shielding constants. These include the standard linear response theory (LRT), the full or external field-dependent unitary transformations of the Dirac operator, as well as the orbital decomposition approach. In contrast with LRT, the latter schemes take explicitly into account both the kinetic and magnetic balances between the large and small components of the Dirac spinors, and are therefore much less demanding on the basis sets. In addition, the diamagnetic contributions, which are otherwise "missing" in LRT, appear naturally in the latter schemes. Nevertheless, the definitions of paramagnetic and diamagnetic terms are not the same in the different schemes, but the difference is only of O(c(-2)) and thus vanishes in the nonrelativistic limit. It is shown that, as an operator theory, the full field-dependent unitary transformation approach cannot be applied to singular magnetic fields such as that due to the magnetic point dipole moment of a nucleus. However, the inherent singularities can be avoided by the corresponding matrix formulation (with a partial closed summation). All the schemes are combined with the Dirac-Kohn-Sham ansatz for ground state calculations, and by using virtually complete basis sets a new and more accurate set of absolute nuclear magnetic resonance shielding scales for the rare gases He-Rn have been established.