Ab initio paramagnetic NMR shifts via point-dipole approximation in a large magnetic-anisotropy Co(ii) complex

Abstract

Transition metal complexes can possess a large magnetic susceptibility anisotropy, facilitating applications such as paramagnetic tags or shift agents in nuclear magnetic resonance (NMR) spectroscopy. Due to its g-shift and zero-field splitting (ZFS) we demonstrate on a Co(ii) clathrochelate with an aliphatic 16-carbon chain, a modern approach for ab initio calculation of paramagnetic susceptibility. Due to its large anisotropy, large linear dimension but relatively low number of atoms, the chosen complex is especially well-suited for testing the long-range point-dipole approximation (PDA) for the pseudocontact shifts (PCSs) of paramagnetic NMR. A static structure of the complex is used to compare the limiting long-distance PDA with full first-principles quantum-mechanical calculation. A non-symmetric formula for the magnetic susceptibility tensor is necessary to be consistent with the latter. Comparison with experimental shifts is performed by conformational averaging over the chain dynamics using Monte Carlo simulation. We observe satisfactory accuracy from the rudimentary simulation and, more importantly, demonstrate the fast applicability of the ab initio PDA.

Solution of a Puzzle: High-Level Quantum-Chemical Treatment of Pseudocontact Chemical Shifts Confirms Classic Semiempirical Theory

“…The zeroth-order eigenfunctions and energies in eq 6 are derived from the zeroth-order Hamiltonian in the SH approximation, H spin (0) = S•D•S. The analogous SH expression for the susceptibility tensor is 28,29…”

“…The appearance of this unsymmetrical tensor was considered a necessary consequence of the more rigorous QC treatment compared with the "semiempirical" eq 1. 26,28,30 The two approaches are ostensibly different. 26 Several recent papers prefer the use of eq 8 because it seemingly gives better agreement with the experimental data.…”

Pseudocontact shifts and paramagnetic susceptibility in semiempirical and quantum chemistry theories

“…essentially outside the room temperature thermal bath. 31 Since the submission of this manuscript, two important papers 37,38 and a review 39 were published dealing with the analysis of the pseudocontact shifts against the g and ZFS tensors, confirming the need of clarifying which relationship should be used to obtain the pseudocontact shifts from the EPR tensors. One paper, by Grandinetti and coworkers, 38 shows that the 2 H paramagnetic shifts measured for first row transition metal (manganese, iron, cobalt, nickel, or copper) chloride dihydrates can be well interpreted using the SE Kurland-McGarvey equation, i.e.…”

“…A second paper, by Mareš and Vaara, 37 presents QC calculations for the prediction of the pseudocontact shifts measured for a cobalt(II) complex with an aliphatic 16-carbon-atom chain attached to it. This system was chosen because it contains atoms far enough from the metal so as paramagnetic shifts are not affected by Fermi-contact contributions and the point-dipole approximation is valid.…”

“…growing QC-based community where a distinct theory framework is being used. 7,10,[23][24][25][26][27][28][29][30][31]37 We have shown using the spin Hamiltonian formalism that the two frameworks imply two different equations for pseudocontact shift where the former depends on the anisotropy of a symmetric paramagnetic susceptibility tensor 𝛘 and the latter on the anisotropy of a previously introduced 31 non-symmetric 𝛘′ tensor, differing from 𝛘 by a missing factor 𝐠 𝑔 ⁄ (see Fig. 3).…”