A partial differential equation for pseudocontact shift

TL;DR

This paper derives an elliptic partial differential equation governing pseudocontact shifts, facilitating easier prediction and analysis of experimental data in complex systems with multiple unpaired electron centers.

Contribution

It introduces a novel PDE framework for modeling pseudocontact shifts, linking them to the Hessian of electron probability density, advancing theoretical understanding and practical analysis.

Findings

Derived a PDE for PCS based on electron density Hessian

Enables straightforward PCS prediction in complex systems

Provides new tools for analyzing experimental PCS data

Abstract

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction as well as analysis of experimental PCS data in systems with multiple and / or distributed unpaired electron centres.