Regularised density-potential inversion for periodic systems: application to exact exchange in one dimension

Le résumé fourni par la source

A detailed convex analysis-based formulation of density-functional theory forperiodic systems in arbitrary dimensions is presented. The electron-electroninteraction is taken to be of Yukawa type, harmonising with underlying functionspaces for densities and wave functions. Moreau--Yosida regularisation of theunderlying non-interacting density functionals is then considered, allowing usto recast the Hohenberg--Kohn mapping in a form that is insensitive toperturbations (non-expansiveness) and lends itself to numerical implementation.The general theory is exemplified with a numerical Hartree--Fock implementationfor one-dimensional systems. We discuss in particular the challenge ofself-consistent field optimisation in calculations related to the regularisednoninteracting Hohenberg--Kohn map. The implementation is used to demonstratethat it is practically feasible to recover local Kohn--Sham potentialsreproducing the effects of exact exchange within this scheme, which provides aproof-of-principle for recovering the exchange-correlation potential at moreaccurate levels of theory. Error analysis is performed for the regularisedinverse Kohn--Sham algorithm by quantifying, both theoretically andnumerically, how perturbations of the input ground-state density propagatethrough the regularised density-to-potential map.

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