Analysis of singular operators in the relativistic calculation of magnetic molecular properties

In the relativistic theory of magnetic molecular properties which involve the magnetic field of a magnetic nucleus, difficulties associated with the divergence of four-component Dirac spinors in the vicinity of the nucleus need be considered with care. Within the point dipole model of the nucleus, singular operators may be involved. This is the case, for instance, of the relativistic calculation of the nuclear magnetic shielding tensor and indirect spin-spin coupling tensor in the context of Kutzelnigg's minimal coupling approach. We show that matrix elements of the magnetic interaction yield divergent values for every single Fermi contact, spin dipolar, paramagnetic spin orbit, and Kutzelnigg's anisotropic Dirac's delta operator. However, when all terms are added together the divergent results cancel each other and a finite convergent result is obtained. It is concluded that Kutzelnigg's minimal coupling approach can be safely applied in the case of a point dipole model of the nucleus, and numerical results should be equivalent to those of the direct linear response approach for the operator V=e alpha center dot A. The importance of the inclusion of the anisotropic Dirac's delta operator is emphasized.