Impact of the current density on paramagnetic NMR properties

17 June 2022, Version 1
This content is a preprint and has not undergone peer review at the time of posting.


Meta-generalized gradient approximations (meta-GGAs) and local hybrid functionals generally depend on the kinetic energy density τ. For magnetic properties, this necessitates generalizations to ensure gauge invariance. In most implementations, τ is generalized by incorporating the external magnetic field. However, this introduces artifacts in the response of the density matrix and does not satisfy the iso-orbital constraint. Here, we extend previous approaches based on the current density to paramagnetic NMR shieldings and EPR g-tensors. The impact is assessed for main-group compounds and transition-metal complexes considering 25 density functional approximations. It is shown that the current density leads to substantial improvements—especially for the popular Minnesota and SCAN functional families. Thus, we strongly recommend to use the current density generalized τ in paramagnetic NMR and EPR calculations with meta-GGAs.


density functional theory
paramagnetic NMR
current-density functional theory
ring current

Supplementary materials

Supporting Information
Complete computational details and data, supporting the findings of the main manuscript.


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