Magnetic Properties of Ni(2+)(aq) from First Principles.

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.

Ferrocene-like iron bis(dicarbollide), [3-Fe(III)-(1,2-C(2)B(9)H(11))(2)](-). The first experimental and theoretical refinement of a paramagnetic (11)B NMR spectrum.

Nuclear magnetic resonance (NMR) of paramagnetic molecules (pNMR) provides detailed information on the structure and bonding of metallo-organic systems. The physical mechanisms underlying chemical shifts are considerably more complicated in the presence of unpaired electrons than in the case of diamagnetic compounds. We report for the first time a combined first-principles theoretical as well as experimental liquid-state (11)B NMR study of a paramagnetic compound, applied on the [3-Fe(III)-(1,2-C(2)B(9)H(11))(2)](-) metallaborane, which is an electronically open-shell structure where the iron centre binds two hemispherical boron-carbon cages. We show that this combined theoretical and experimental analysis constitutes a firm basis for the assignment of experimental (11)B NMR chemical shifts in paramagnetic metallaboranes. In the calculations, the roles of the different physical contributions to the pNMR chemical shift are elaborated, and the performance of different popular exchange-correlation functionals of density-functional theory as well as basis sets, are evaluated. A dynamic correction to the calculated shifts via first-principles molecular dynamics simulations is found to be important. Solvent effects on the chemical shifts were computed and found to be of minor significance.

Dynamics and magnetic resonance properties of Sc3C2@C80 and its monoanion.

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.

Nuclear magnetic resonance chemical shift in an arbitrary electronic spin state.

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.

Density-functional calculations of relativistic spin-orbit effects on nuclear magnetic shielding in paramagnetic 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.