Fully relativistic theories and methods for NMR parameters

Nuclear magnetic shielding and spin-spin coupling constants are intrinsically all-electron relativistic properties and demand in principle fully relativistic treatments. Here, the magnetic balance (MB) condition plays an essential role, both conceptually and computationally. The various formulations can be unified in terms of the idea of orbital decomposition. Further combined with the ansatz of gauge-including atomic orbitals (GIAO) for distributed gauge origins leads to very efficient four-component relativistic methods at both the mean-field and correlated levels. To illustrate the latter, the no-pair MB-GIAO-MP2 expressions for nuclear shieldings are derived in two different ways, one with the derivative technique and the other through the induced current. Due to the non-variational nature of MP2, the two expressions are not identical. The current-dependent expression is much simpler and appears more natural in view of the experimental measurement.