Assignment of solid-state 13C and 1H NMR spectra of paramagnetic Ni(II) acetylacetonate complexes aided by first-principles computations.

Recent advances in computational methodology allowed for first-principles calculations of the nuclear shielding tensor for a series of paramagnetic nickel(II) acetylacetonate complexes, [Ni(acac)2L2] with L = H2O, D2O, NH3, ND3, and PMe2Ph have provided detailed insight into the origin of the paramagnetic contributions to the total shift tensor. This was employed for the assignment of the solid-state 1,2H and 13C MAS NMR spectra of these compounds. The two major contributions to the isotropic shifts are by orbital (diamagnetic-like) and contact mechanism. The orbital shielding, contact, as well as dipolar terms all contribute to the anisotropic component. The calculations suggest reassignment of the 13C methyl and carbonyl resonances in the acac ligand [Inorg. Chem.53, 2014, 399] leading to isotropic paramagnetic shifts of δ(13C) ≈ 800-1100 ppm and ≈180-300 ppm for 13C for the methyl and carbonyl carbons located three and two bonds away from the paramagnetic Ni(II) ion, respectively. Assignment using three different empirical correlations, i.e., paramagnetic shifts, shift anisotropy, and relaxation (T1) were ambiguous, however the latter two support the computational results. Thus, solid-state NMR spectroscopy in combination with modern quantum-chemical calculations of paramagnetic shifts constitutes a promising tool for structural investigations of metal complexes and materials.

Relativistic Approximations to Paramagnetic NMR Chemical Shift and Shielding Anisotropy in Transition Metal Systems.

We apply approximate relativistic methods to calculate the magnetic property tensors, i.e., the g-tensor, zero-field splitting (ZFS) tensor (D), and hyperfine coupling (HFC) tensors, for the purpose of constructing paramagnetic nuclear magnetic resonance (pNMR) shielding tensors. The chemical shift and shielding anisotropy are calculated by applying a modern implementation of the classic Kurland-McGarvey theory ( J. Magn. Reson. 1970 , 2 , 286 ), which formulates the shielding tensor in terms of the g- and HFC tensors obtained for the ground multiplet, in the case of higher than doublet multiplicity defined by the ZFS interaction. The g- and ZFS tensors are calculated by ab initio complete active space self-consistent field and N-electron valence-state perturbation theory methods with spin-orbit (SO) effects treated via quasidegenerate perturbation theory. Results obtained with the scalar relativistic (SR) Douglas-Kroll-Hess Hamiltonian used for the g- and ZFS tensor calculations are compared with nonrelativistically based computations. The HFC tensors computed using the fully relativistic four-component matrix Dirac-Kohn-Sham approach are contrasted against perturbationally SO-corrected nonrelativistic results in the density functional theory framework. These approximations are applied on paramagnetic metallocenes (MCp2) (M = Ni, Cr, V, Mn, Co, Rh, Ir), a Co(II) pyrazolylborate complex, and a Cr(III) complex. SR effects are found to be small for g and D in these systems. The HFCs are found to be more influenced by relativistic effects for the 3d systems. However, for some of the 3d complexes, nonrelativistic calculations give a reasonable agreement with the experimental chemical shift and shielding anisotropy. The influence of scalar relativity is strong for the 5d IrCp2 system. This mixed ab initio/DFT technique, with a fully relativistic method used for the critical HFC tensor, should be useful for the treatment of both electron correlation and relativistic effects at a reasonable computational cost to compute the pNMR shielding tensors in transition metal systems.

Paramagnetic Enhancement of Nuclear Spin-Spin Coupling.

We present a derivation and computations of the paramagnetic enhancement of the nuclear magnetic resonance (NMR) spin-spin coupling, which may be expressed in terms of the hyperfine coupling (HFC) and (for systems with multiple unpaired electrons) zero-field splitting (ZFS) tensors. This enhancement is formally analogous to the hyperfine contributions to the NMR shielding tensor as formulated by Kurland and McGarvey. The significance of the spin-spin coupling enhancement is demonstrated by using a combination of density-functional theory and correlated ab initio calculations, to determine the HFC and ZFS tensors, respectively, for two paramagnetic 3d metallocenes, a CrII(acac)2 complex, a Co(II) pyrazolylborate complex, and a lanthanide system, Gd-DOTA. Particular attention is paid to relativistic effects in HFC tensors, which are calculated using two methods: a nonrelativistic method supplemented by perturbational spin-orbit coupling corrections, and a fully relativistic, four-component matrix-Dirac-Kohn-Sham approach. The paramagnetic enhancement lacks a direct dependence on the distance between the coupled nuclei, and represents more the strength and orientation of the individual hyperfine couplings of the two nuclei to the spin density distribution. Therefore, the enhancement gains relative importance as compared to conventional coupling as the distance between the nuclei increases, or generally in the cases where the conventional coupling mechanisms result in a small value. With the development of the experimental techniques of paramagnetic NMR, the more significant enhancements, e.g., of the 13C13C couplings in the Gd-DOTA complex (as large as 9.4 Hz), may eventually become important.

Magnetic couplings in the chemical shift of paramagnetic NMR.

We apply the Kurland-McGarvey (J. Magn. Reson. 1970, 2, 286) theory for the NMR shielding of paramagnetic molecules, particularly its special case limited to the ground-state multiplet characterized by zero-field splitting (ZFS) interaction of the form S·D·S. The correct formulation for this problem was recently presented by Soncini and Van den Heuvel (J. Chem. Phys. 2013, 138, 054113). With the effective electron spin quantum number S, the theory involves 2S+1 states, of which all but one are low-lying excited states, between which magnetic couplings take place by Zeeman and hyperfine interactions. We investigate these couplings as a function of temperature, focusing on both the high- and low-temperature behaviors. As has been seen in work by others, the full treatment of magnetic couplings is crucial for a realistic description of the temperature behavior of NMR shielding up to normal measurement temperatures. At high temperatures, depending on the magnitude of ZFS, the effect of magnetic couplings diminishes, and the Zeeman and hyperfine interactions become effectively averaged in the thermally occupied states of the multiplet. At still higher temperatures, the ZFS may be omitted altogether, and the shielding properties may be evaluated using a doublet-like formula, with all the 2S+1 states becoming effectively degenerate at the limit of vanishing magnetic field. We demonstrate these features using first-principles calculations of Ni(II), Co(II), Cr(II), and Cr(III) complexes, which have ZFS of different sizes and signs. A non-monotonic inverse temperature dependence of the hyperfine shift is predicted for axially symmetric integer-spin systems with a positive D parameter of ZFS. This is due to the magnetic coupling terms that are proportional to kT at low temperatures, canceling the Curie-type 1/kT prefactor of the hyperfine shielding in this case.

¹H Chemical Shifts in Paramagnetic Co(II) Pyrazolylborate Complexes: A First-Principles Study.

We apply the theory of the nuclear magnetic resonance (NMR) chemical shift for paramagnetic systems to demanding cobalt(II) complexes. Paramagnetic NMR (pNMR) chemical shift results by density-functional theory (DFT) can be very far from the experimental values. Therefore, it is of interest to investigate the applicability of electron-correlated ab initio computational methods to achieve useful accuracy. Here, we use ab initio wave function based electronic structure methods to calculate the pNMR chemical shift within the theoretical framework established recently. We applied the N-electron valence-state perturbation theory (NEVPT2) on three Co(II) systems, where the active space of the underlying complete active space self-consistent field (CASSCF) wave function consists of seven electrons in the five metal 3d orbitals. These complexes have the S = 3/2 electronic ground state consisting of two doublets separated by zero-field splitting (ZFS). To calculate the hyperfine coupling tensor A, DFT was used, while the g- and ZFS-tensors were calculated using the ab initio CASSCF and NEVPT2 methods. These results were combined to obtain the total chemical shifts. The shifts obtained from these calculations are in generally good agreement with the experimental results, in some cases suggesting a reassignment of the signals. The accuracy of this mixed ab initio/DFT approach is very promising for further applications to demanding pNMR problems involving transition metals.