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We present a theory of nuclear magnetic resonance (NMR) shielding tensors forelectronic states with arbitrary degeneracy. The shieldings are here expressedin terms of generalized Zeeman ($g^{(k)}$) and hyperfine ($A^{(k)}$) tensors,of all ranks $k$ allowed by the size of degeneracy. Contrary to recentproposals [T. O. Pennanen and J. Vaara, Phys. Rev. Lett. 100, 133002 (2008)],our theory is valid in the strong spin-orbit coupling limit. Ab initiocalculations for the 4-fold degenerate $\Gamma_8$ ground state oflanthanide-doped fluorite crystals CaF$_2$:Ln (Ln = Pr$^{2+}$, Nd$^{3+}$,Sm$^{3+}$, and Dy$^{3+}$) show that previously neglected contributions canaccount for more than 50% of the paramagnetic shift.

Theory of NMR chemical shift in an electronic state with arbitrary degeneracy