Fully relativistic calculations of NMR shielding tensors using restricted magnetically balanced basis and gauge including atomic orbitals

A recently developed relativistic four-component density functional method for calculation of nuclear magnetic resonance (NMR) shielding tensors using restricted magnetically balanced basis sets for the small component (mDKS-RMB) was extended to incorporate the gauge including atomic orbitals (GIAO) approach. The combined method eliminates a strong dependence of the results, calculated with a finite basis set, on the choice of the gauge origin for the magnetic potential of a uniform external magnetic field. Benchmark relativistic calculations have been carried out for xenon dimer and the HX series (X=F, Cl, Br, I), where spin-orbit effects are known to be very pronounced for hydrogen shieldings. Our results clearly demonstrate that shieldings calculated at the four-component level with a common gauge (i.e., without GIAO, IGLO, or similar methods to treat the gauge problem) depend dramatically on the choice of the common gauge. The GIAO approach solves the problem in fully relativistic calculations as it does in the nonrelativistic case.