Hidden Relaxation Term in Approximate Treatments of Responses to Electric and Magnetic Fields

TL;DR

This paper reveals a hidden relaxation term affecting electric and magnetic response calculations in the modern theory of polarization and magnetization, explaining discrepancies in reciprocal-space sampling and providing conditions to avoid its computation.

Contribution

It identifies a previously overlooked relaxation contribution in approximate response calculations, improving the understanding of non-local Hamiltonian effects.

Findings

Hidden relaxation term explains sampling discrepancies

Affects both magnetic and electric response calculations

Conditions provided to avoid calculating the relaxation term

Abstract

Recently a generalization of the ``\textit{modern theory of orbital magnetization}'' to include non-local Hamiltonians (e.g. hybrid functionals of the generalized Kohn-Sham theory) was provided for magnetic response properties. Results indicated inequivalence between sampling of direct and reciprocal spaces for those calculations far from the complete basis set limit. We show that this can be explained by a hidden ``relaxation'' contribution to the reciprocal-space derivatives. The missing relaxation term is shown to (generally) affect the results of calculations of not only magnetic, but also electric response properties, within the context of the ``\textit{modern theory of polarization}''. Necessary conditions are provided to permit avoiding the calculation of the hidden relaxation term.