Paramagnetic Enhancement of Nuclear Spin–Spin Coupling

Abstract

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 spinspin 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 Cr(II)(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, 4-component matrixDirac-Kohn-Sham approach. The paramagnetic enhancement lacks a direct dependence on the

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

“…The corresponding methodology was recently applied to the calculation of pNMR spin−spin coupling enhancement. 59 We demonstrate this combined methodology with calculations on paramagnetic metallocenes that have been selected, on the one hand, with the central metal ion across the 3d period and, on the other hand, down group IX of the periodic table with 3d, 4d, and 5d doublet metallocenes. These metallocenes have already been investigated in pNMR shielding calculations in many other studies 4,12,13,44,[48][49][50]60 and represent different spin states, i.e., S = 1 (nickelocene and chromocene), 3/2 (vanadocene), and 5/2 (manganocene), all with the central atom in the 3d period as well as the group IX S = 1/2 cobaltocene, rhodocene, and iridocene.…”

“…We believe that the influence of SR effects on pNMR shielding tensors has not previously been subjected to such a systematic investigation. The corresponding methodology was recently applied to the calculation of pNMR spin–spin coupling enhancement …”

Paramagnetic Cobalt(II) Complexes with Cyclam Derivatives: Toward 19F MRI Contrast Agents

“…The large C9 paramagnetic shift and the possibility to measure the 1 J CF coupling in both paramagnetic trans -[Co II ( te2f2p )] 2– ( 1 J CF = 268 Hz) and diamagnetic trans -[Co III ( te2f2p )] − ( 1 J CF = 282 Hz) variants of the complex suggest an intriguing question of whether the 1 J CF coupling difference between the paramagnetic and diamagnetic forms, Δ J = 1 J CF para – 1 J CF dia = −14 Hz, could be ascribed to paramagnetic enhancement. Applying the recent theory of paramagnetically enhanced J -coupling, we found that the 1 J CF paramagnetic enhancement is too small, on the order of −0.25 Hz. The observed 1 J CF coupling difference thus has a different cause, likely structural, related to the difference in charge of the central ion.…”

Quantum-Chemical Approach to Nuclear Magnetic Resonance of Paramagnetic Systems

“…Often continuous solids, as opposed to materials consisting of a condensed assembly of molecules, are experimentally interesting, and for this end the molecular approach of Kurland-McGarvey has been generalised for periodic boundary conditions (PBC, Mondal & Kaupp, 2018). The (Cherry, Rouf & Vaara, 2017) involving the hyperfine couplings A K and A L of both the coupled nuclei with the unpaired electron spins, as well as the same dyadic of the effective electron spin operator as in the corresponding theory of the shielding tensor (Figure 2). (Right) Nickelocene system (S = 1), in which the predicted paramagnetic enhancements of the spin-spin coupling constants greatly exceed the magnitude of the conventional coupling constants for couplings across the metal centre, between nuclei located in the different cyclopentadienyl rings ( m J KL ).…”