Pseudocontact shifts and paramagnetic susceptibility in semiempirical and quantum chemistry theories

TL;DR

This paper compares semiempirical and quantum chemistry approaches to calculating pseudocontact shifts, revealing differences in tensor symmetry and the influence of orbital contributions on hyperfine coupling.

Contribution

It provides a detailed analysis of the foundational differences between semiempirical and quantum chemistry theories for pseudocontact shifts, especially regarding tensor symmetry and spin-orbit coupling.

Findings

Quantum chemistry pseudocontact shifts scale with a non-symmetric tensor.

Semiempirical theory assumes a symmetric paramagnetic susceptibility tensor.

Differences stem from the treatment of orbital contributions to hyperfine coupling.

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 (R.J. Kurland and B.R. McGarvey, J. Magn. Reson. 2, 286 (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 g/ge 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.