Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension
arXiv:2510.24330 · doi:10.1063/5.0310171
Abstract
A detailed convex analysis-based formulation of density-functional theory for periodic systems in arbitrary dimensions is presented. The electron-electron interaction is taken to be of Yukawa type, harmonising with underlying function spaces for densities and wave functions. Moreau--Yosida regularisation of the underlying non-interacting density functionals is then considered, allowing us to recast the Hohenberg--Kohn mapping in a form that is insensitive to perturbations (non-expansiveness) and lends itself to numerical implementation. The general theory is exemplified with a numerical Hartree--Fock implementation for one-dimensional systems. We discuss in particular the challenge of self-consistent field optimisation in calculations related to the regularised noninteracting Hohenberg--Kohn map. The implementation is used to demonstrate that it is practically feasible to recover local Kohn--Sham potentials reproducing the effects of exact exchange within this scheme, which provides a proof-of-principle for recovering the exchange-correlation potential at more accurate levels of theory. Error analysis is performed for the regularised inverse Kohn--Sham algorithm by quantifying, both theoretically and numerically, how perturbations of the input ground-state density propagate through the regularised density-to-potential map.
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