New Relativistic Theory For NMR Shieldings

Theoretical calculations, nonrelativistic or relativistic, on NMR spectroscopic pa-rameters such as shielding tensors have a long history. Surprisingly, however, the mostrelativistic method, four-component relativistic theory, for magnetic properties has notbeen developed to the same level of sophistication as for electric properties. The un-derlying reason is that, compared to an electric perturbation, a magnetic perturbationhas a much stronger in?uence on the coupling of the large and small components ofthe Dirac spinor, leading to the fact that the contributions of negative energy statesto magnetic properties are of O(c⁰) instead of O(c^-4) as for electric properties. Thatis, if the contributions of negative energy states are neglected, the entire diamagneticterm will be missed, even at the nonrelativistic limit. The key issue is therefore howto account for such contributions in a four-component relativistic treatment. Standardlinear response theory is just painful for practical use: It requires una?ordable largebasis sets of high angular momenta to compensate for the lack of the magnetic bal-ance condition. Here we propose several novel schemes to take explicitly into accountthe magnetic balance condition, in addition to the kinetic balance condition. Theseinclude the orbital decomposition approach, external-field dependent unitary transfor-mation at operator level, and the full-field dependent unitary transformation but atmatrix level. The latter two are generalizations of Kutzelnigg's original formulationfor a single regular field. The corresponding approximate variants are also obtained byconsistent neglect of negative energy states, leading to errors of O(c^-2) or O(c^-4). Allthe variants can readily be extended to other magnetic properties. It can therefore beclaimed that relativistic theory for magnetic properties has been solved. As a matter offact, four-component relativistic theory for magnetic properties has become as easy asfor electric properties-A standard triple-zeta basis set already leads to decent results!...