We present a general and systematic electronic structure theory of the nuclear magnetic resonance shielding tensor and the associated chemical shift for paramagnetic atoms, molecules, and nonmetallic solids. The approach is for the first time rigorous for an arbitrary spin state as well as arbitrary spatial symmetry and is formulated without reference to spin susceptibility. The leading-order magnetic-field dependence of shielding is derived. The theory is demonstrated by first principles calculations of organometallic molecules.

Terms arising from the relativistic spin-orbit effect on both hyperfine and Zeeman interactions are introduced to density-functional theory calculation of nuclear magnetic shielding in paramagnetic molecules. The theory is a generalization of the former nonrelativistic formulation for doublet systems and is consistent to O(alpha4), the fourth power of the fine structure constant, for the spin-orbit terms. The new temperature-dependent terms arise from the deviation of the electronic g tensor from the free-electron g value as well as spin-orbit corrections to hyperfine coupling tensor A, the latter introduced in the present work. In particular, the new contributions include a redefined isotropic pseudocontact contribution that consists of effects due to both the g tensor and spin-orbit corrections to hyperfine coupling. The implementation of the spin-orbit terms makes use of all-electron atomic mean-field operators and/or spin-orbit pseudopotentials. Sample results are given for group-9 metallocenes and a nitroxide radical. The new O(alpha4) corrections are found significant for the metallocene systems while they obtain small values for the nitroxide radical. For the isotropic shifts, none of the three beyond-leading-order hyperfine contributions are negligible.

We report density functional theory (DFT) studies on the endohedral scandium carbide fullerene Sc3C2@C80 and its monoanion [Sc3C2@C80](-). The system consisting of a Sc3C2 moiety inside the Ih C80 fullerene has been studied by using first principles molecular dynamics simulations at the DFT level. On the picosecond time scale, the triangle defined by the scandium atoms is seen to jump between orientations along the equatorial six-membered ring belt of the cage. The confined carbide unit, in turn, is engaged in a flipping motion through the Sc3 plane. In contrast to the equilibrium geometry optimisations using large basis sets that predict a trigonal bipyramidal structure, a planar Sc3C2-moiety is preferred during the finite-temperature simulation. In the molecular dynamics picture, Sc3C2@C80 is best described as an equilibrium between the two static minimum structures. Calculations of the vibrational frequencies show that the earlier predicted C2 and C2v symmetric isomers are in fact saddle points, with one imaginary normal mode frequency that is related to the flipping motion of the confined carbon dimer. Reoptimisation revealed two new minimum energy structures where the C2 unit is tilted with respect to its orientation in the earlier suggested higher-symmetry structures. The nature of the bonding in the static structures of the two isomers of Sc3C2@C80 has been investigated using the electron localisation function and natural population analysis. Some increased electron pair localisation is detected on the six-membered rings closest to the Sc atoms. 13C nuclear magnetic resonance (NMR) chemical shifts have been calculated for the closed-shell monoanion of Sc3C2@C80. The 13C shifts were also calculated for Sc2C2@C84, for further comparison to experimentally measured spectra. The confined carbon atoms are strongly deshielded in these metallofullerenes, implying an incorrect earlier interpretation of the experimental 13C NMR spectrum of Sc2C2@C84. The neutral Sc3C2@C80 system with one unpaired electron is further characterised by calculating the hyperfine coupling constants, the g tensor, as well as paramagnetic NMR (pNMR) 13C shifts for both static isomers. The chemical shifts of the confined carbon atoms and the hyperfine coupling constants of all the confined atoms are strongly dependent on the conformation of the Sc3C2 moiety. Consequently, dynamical effects are expected to be important in the modelling of the magnetic properties of endohedral scandium carbide fullerenes. The two low-lying isomers have rather different pNMR 13C shifts, implying the potential of this method in structural assignment.

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.

The aqueous solution of the Ni(2+) ion was investigated using a first principles molecular dynamics (FPMD) simulation based on periodic density-functional theory (DFT) calculations. Statistical averages of the magnetic properties corresponding to the triplet spin state of the ion, the hyperfine coupling, g and zero-field splitting tensors, as well as the resulting paramagnetic nuclear magnetic resonance (pNMR) shielding terms were calculated using DFT from instantaneous simulation snapshots extracted from the FPMD trajectory. We report comprehensive tests of the reliability of systematically selected DFT functionals for the properties. The isotropic nuclear shielding of the (17)O nuclei can be obtained with good predictive power. The accuracy of the calculated (1)H shieldings is limited by the fact that the spin-density on the proton sites is not reproduced reliably with the tested functionals, rendering the dominant Fermi contact isotropic shielding term less well-defined. On the other hand, the dominant spin-dipole term of the shielding anisotropy, which gives a practically vanishing isotropic contribution, can be obtained with good reliability for both the (1)H and (17)O nuclei. The anisotropic shielding tensor can be thus utilized reliably in the calculation of Curie-type paramagnetic relaxation. We discuss the evolution of the pNMR properties through the first and second solvation shells of the ion, toward the bulk solvent. The magnetic properties of the dominant, six-coordinated solution are compared to those of the metastable, 5-fold coordinated intermediate occurring in the dissociative exchange process.