Using a recently proposed equation for NMR nuclear magnetic shielding for molecules with unpaired electrons [A. Soncini and W. Van den Heuvel, J. Chem. Phys. 138, 021103 (2013)], equations for the temperature (T) dependent isotropic shielding for multiplets with an effective spin S equal to 1/2, 1, 3/2, 2, and 5/2 in terms of electron paramagnetic resonance spin Hamiltonian parameters are derived and then expanded in powers of 1/T. One simplifying assumption used is that a matrix derived from the zero-field splitting (ZFS) tensor and the Zeeman coupling matrix (g-tensor) share the same principal axis system. The influence of the rhombic ZFS parameter E is only investigated for S = 1. Expressions for paramagnetic contact shielding (from the isotropic part of the hyperfine coupling matrix) and pseudo-contact or dipolar shielding (from the anisotropic part of the hyperfine coupling matrix) are considered separately. The leading order is always 1/T. A temperature dependence of the contact shielding as 1/T and of the dipolar shielding as 1/T(2), which is sometimes assumed in the assignment of paramagnetic chemical shifts, is shown to arise only if S ≥ 1 and zero-field splitting is appreciable, and only if the Zeeman coupling matrix is nearly isotropic (Δg = 0). In such situations, an assignment of contact versus dipolar shifts may be possible based only on linear and quadratic fits of measured variable-temperature chemical shifts versus 1/T. Numerical data are provided for nickelocene (S = 1). Even under the assumption of Δg = 0, a different leading order of contact and dipolar shifts in powers of 1/T is not obtained for S = 3/2. When Δg is not very small, dipolar and contact shifts both depend in leading order in 1/T in all cases, with sizable contributions in order 1/T(n) with n = 2 and higher.

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A theory for the nuclear chemical shifts of molecules in arbitrary spin states is applied to a set of paramagnetic organometallic complexes of 3d metals. Ligand chemical shifts are calculated and analyzed using Kohn-Sham (KS) density functional theory with and without relativistic corrections. The roles of the KS delocalization error, Gaussian-type versus Slater-type basis sets, relativistic effects (scalar and spin-orbit), and zero field splitting (ZFS) are investigated. A strong functional dependence of the chemical shifts is apparent and correlated with the delocalization error. The functional dependence is between one and two orders of magnitude larger than variations of the NMR shifts due the other influences that are investigated. ZFS effects are negligible in the determination of the NMR chemical shifts of the complexes except at very low temperatures. The DFT calculated shifts agree reasonably well with experiment. A 73 ppm difference in the NMR shifts of the two protons in the amide groups of a high-spin Fe(ii) macrocycle complex arises from selective O → Fe dative bonding that only involves the transfer of β spin density, along with orbital delocalization throughout the ligand bonding framework which electronically couples the coordinating oxygen lone pair orbitals directly to the amide trans proton.