Relativistic theory of nuclear shielding in one-electron atoms 1. Theoretical foundations, and first-order terms

The nuclear shielding in NMR spectroscopy is given in relativistic theory ( Pyper, N. C., 1983, Chem. Phys. Lett., 96, 204) as the sum of the exact rel ativistic analogues of the non-relativistic diamagnetic and paramagnetic te rms augmented by a further purely relativistic term. In this paper this the ory, based on the Gordon decomposition of the Dirac current, is extended to encompass the point charge-point dipole model of the nucleus, the previous formulation (Pyper, 1983) being restricted to spatially extended descripti ons of the nuclear charge and magnetization. For the point nucleus case, an alytical expressions for both the purely relativistic shielding contributio n and diamagnetic term are derived for all orbitals. The result for the dia magnetic shielding is derived by invoking the relativistic virial theorem, and thus depends only on the orbital energy and magnetic quantum number nz. Therefore it shows, for given m, the same 'accidential' degeneracy between orbitals differing in the sign of the quantum number kappa as the energy. The purely relativistic contribution to the shielding is shown to differ fr om the electronic contribution to the hyperfine energy by a factor of only m multiplied by fundamental constants. The present purely relativistic term is shown to equal the previous result (Pyper, 1953) even though appearing in a different form. For the interaction with a uniform magnetic field the relativistically exact Hamiltonian obtained from the Gordon decomposition i s used with the virial theorem to derive a new expression for the g factor for all orbitals. The resulting simple expression depends only on the orbit al energy in addition to the quantum numbers kappa and m.