Magnetic Properties of Ni2+(aq) from First Principles

Paramagnetic NMR in solution and the solid state

The field of paramagnetic NMR has expanded considerably in recent years. This review addresses both the theoretical description of paramagnetic NMR, and the way in which it is currently practised. We provide a review of the theory of the NMR parameters of systems in both solution and the solid state. Here we unify the different languages used by the NMR, EPR, quantum chemistry/DFT, and magnetism communities to provide a comprehensive and coherent theoretical description. We cover the theory of the paramagnetic shift and shift anisotropy in solution both in the traditional formalism in terms of the magnetic susceptibility tensor, and using a more modern formalism employing the relevant EPR parameters, such as are used in first-principles calculations. In addition we examine the theory first in the simple non-relativistic picture, and then in the presence of spin-orbit coupling. These ideas are then extended to a description of the paramagnetic shift in periodic solids, where it is necessary to include the bulk magnetic properties, such as magnetic ordering at low temperatures. The description of the paramagnetic shift is completed by describing the current understanding of such shifts due to lanthanide and actinide ions. We then examine the paramagnetic relaxation enhancement, using a simple model employing a phenomenological picture of the electronic relaxation, and again using a more complex state-of-the-art theory which incorporates electronic relaxation explicitly. An additional important consideration in the solid state is the impact of bulk magnetic susceptibility effects on the form of the spectrum, where we include some ideas from the field of classical electrodynamics. We then continue by describing in detail the solution and solid-state NMR methods that have been deployed in the study of paramagnetic systems in chemistry, biology, and the materials sciences. Finally we describe a number of case studies in paramagnetic NMR that have been specifically chosen to highlight how the theory in part one, and the methods in part two, can be used in practice. The systems chosen include small organometallic complexes in solution, solid battery electrode materials, metalloproteins in both solution and the solid state, systems containing lanthanide ions, and multi-component materials used in pharmaceutical controlled-release formulations that have been doped with paramagnetic species to measure the component domain sizes.

Kohn–Sham calculations of NMR shifts for paramagnetic 3d metal complexes: protocols, delocalization error, and the curious amide proton shifts of a high-spin iron(ii) macrocycle complex

Ligand chemical shifts (pNMR shifts) are analyzed using DFT. A large difference in the amide proton shifts of a high-spin Fe(ii) complex arises from O → Fe dative bonding which only transfers β spin density to the metal.

Temperature dependence of contact and dipolar NMR chemical shifts in paramagnetic molecules

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.

Characterization of Paramagnetic Reactive Intermediates: Predicting the NMR Spectra of Iron(IV)-Oxo Complexes by DFT

The relative energies of spin states of several iron(IV)-oxo complexes and related species have been calculated with DFT methods by employing the B3LYP* functional. We show that such calculations can predict the correct ground spin state of Fe(IV) complexes and can then be used to determine the (1) H NMR spectra of all spin states; the spectral features are remarkably different, hence calculated paramagnetic (1) H NMR spectra can be used to support the structure elucidation of numerous paramagnetic complexes. Applications to a number of stable and reactive iron(IV)-oxo species are described.

Predicting the spin state of paramagnetic iron complexes by DFT calculation of proton NMR spectra

Many transition-metal complexes easily change their spin state S in response to external perturbations (spin crossover). Determining such states and their dynamics can play a central role in the understanding of useful properties such as molecular magnetism or catalytic behavior, but is often far from straightforward. In this work we demonstrate that, at a moderate computational cost, density functional calculations can predict the correct ground spin state of Fe(ii) and Fe(iii) complexes and can then be used to determine the (1)H NMR spectra of all spin states. Since the spectral features are remarkably different according to the spin state, calculated (1)H NMR resonances can be used to infer the correct spin state, along with supporting the structure elucidation of numerous paramagnetic complexes.

Curie-type paramagnetic NMR relaxation in the aqueous solution of Ni(ii)

The magnetic field of the Curie spin manifests itself as both the pNMR shielding tensor and Curie relaxation, in analogy with CSA relaxation theory.