Density functional calculation of nuclear magnetic resonance chemical shifts

A current-density functional theory for the calculation of nuclear magnetic resonance chemical shifts is presented. If the Kohn–Sham orbitals are expanded in a finite basis set, one of the main problems is the strong dependency of the results with respect to a shift of the gauge origin of the vector potential which describes the external magnetic field. Two computational schemes implementing both the individual gauge for localized orbitals (IGLO) and gauge including atomic orbitals (GIAO) concepts, which overcome this problem by introducing distributed gauge origins, are presented in detail. A comparison of the density functional IGLO and GIAO schemes shows that IGLO is much more efficient if one neglects the current-dependent part of the density functional (as is done in ‘‘uncoupled’’ density functional theory), but that this advantage is less pronounced in the full current-density functional treatment.