Four-component relativistic theory for NMR parameters: Unified formulation and numerical assessment of different approaches

Several four-component relativistic approaches for nuclear magnetic shielding constant have recently been proposed and their formal relationships have also been established [Xiao , J. Chem. Phys. 126, 214101 (2007)]. It is shown here that the approaches can be recast into a unified form via the generic ansatz of orbital decomposition. The extension of the formalisms to magnetizability (and nuclear spin-spin coupling) is straightforward. Exact analytical expressions are also derived for both the shielding constant and magnetizability of the hydrogenlike atom in the ground state. A series of calculations on Rn85+ and Rn is then carried out to reveal the performance of the various methods with respect to the basis set requirement, leading to the conclusion that it is absolutely essential to explicitly account for the magnetic balance condition. However, different ways of doing so lead to quite similar results. It is also demonstrated that only extremely compact negative energy states are important for the total shieldings and their effects are hence essentially canceled out for chemical shifts. This has important implications for further theoretical developments.