Pseudocontact shifts and paramagnetic susceptibility in semiempirical and quantum chemistry theories

Abstract

Pseudocontact shifts are traditionally described as a function of the anisotropy of the paramagnetic susceptibility tensor, according to the semiempirical theory mainly developed by Kurland and McGarvey (Kurland, R. J. & McGarvey, B. R. J. Magn. Reson. 2, 286-301 (1970)). The paramagnetic susceptibility tensor is required to be symmetric. Applying point-dipole approximation to the quantum chemistry theory of hyperfine shift, pseudocontact shifts are found to scale with a non-symmetric tensor that differs by a factor ⁄ from the paramagnetic susceptibility tensor derived within the semiempirical framework. We analyze the foundations of the Kurland-McGarvey pseudocontact shift expression and recall that it is inherently based on the Russell-Saunders (LS) coupling approximation for the spin-orbit coupling. We show that the difference between the semiempirical and quantum chemistry pseudocontact shift expressions arises directly from the different treatment of the orbital contribution to the hyperfine coupling. a)

How the Ligand Field in Lanthanide Coordination Complexes Determines Magnetic Susceptibility Anisotropy, Paramagnetic NMR Shift, and Relaxation Behavior

“…Detailed analyses of PCS data have been undertaken for isostructural complexes, with known solution speciation. ,,− A semiautomated combinatorial assignment procedure using PCS data, XRD structure and NMR relaxation rates to limit the combinatorial space (in Spinach) was deployed for [LnL 8a ], enabling assignment of almost every proton resonance . Subsequently, the traceless part of the magnetic susceptibility tensor was obtained by fitting eq to experimental data, giving excellent agreement ( R 2 > 0.99).…”

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

“…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.…”

“…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. 28,32,33 Even recent and authoritative reviews 29 indirectly contribute to endorsing the use of eq 8.…”

“…28,32,33 Even recent and authoritative reviews 29 indirectly contribute to endorsing the use of eq 8. Therefore, as the use of eq 8 is becoming increasingly attractive and the two equations can lead to significantly different results, 26,35 it is important to establish as soon as possible and beyond doubt which of the two expressions should be used for the calculation of PCSs.…”

“…Equation 8incorporates this orbital contribution in the former but not the latter, i.e., in a very unsymmetrical way. 20,26,35 Starting from these premises, in this Letter we go beyond the previous QC-based treatments in two important aspects: (1) we include in the molecular Hamiltonian the so-called gauge correction terms, 36 which are necessary to preserve gauge invariance in the presence of SOC, and (2) we explicitly include all of the contributions (not only the SD one) to the magnetic hyperfine field and to the A tensor. With regard to the electronic Hamiltonian, we assume the usual nonrelativistic Hamiltonian with magnetic fields incorporated by adding the magnetic vector potential to the canonical momentum operator, supplemented with SOC in the effective nuclear charge approximation.…”