We present the first chemical application of the recent, general theory of the nuclear magnetic resonance shielding and chemical shift in paramagnetic compounds, to a set of nonaxial high-spin metallo-organic complexes. The theory is for the first time rigorous for systems of arbitrary spatial and spin symmetry, and introduces new structure to the isotropic, anisotropic but symmetric, and anisotropic and antisymmetric parts of the shielding tensor. We apply the theory using density functional calculations of the proton chemical shift in a family of nonaxial chromium(III) complexes possessing a quartet ground electronic spin state. We discuss the various contributions to the isotropic chemical shift, and compare the full theory to approximate forms appropriate to the doublet case on the one hand, and to the doublet case at the nonrelativistic limit, on the other hand. The performance of various exchange-correlation functionals in reproducing the recently measured experimental chemical shifts is evaluated.
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