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arXiv · 1804.08793

Generalized Kohn-Sham iteration on Banach spaces

Andre Laestadius·Markus Penz·Erik I. Tellgren·Michael Ruggenthaler·Simen Kvaal·Trygve Helgaker
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Abstract

A detailed account of the Kohn-Sham algorithm from quantum chemistry, formulated rigorously in the very general setting of convex analysis on Banach spaces, is given here. Starting from a Levy-Lieb-type functional, its convex and lower semi-continuous extension is regularized to obtain differentiability. This extra layer allows to rigorously introduce, in contrast to the common unregularized approach, a well-defined Kohn-Sham iteration scheme. Convergence in a weak sense is then proven. This generalized formulation is applicable to a wide range of different density-functional theories and possibly even to models outside of quantum mechanics.

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Andre Laestadius, Markus Penz, Erik I. Tellgren, Michael Ruggenthaler, Simen Kvaal, Trygve Helgaker. 2018-10-17. Generalized Kohn-Sham iteration on Banach spaces. https://doi.org/10.1063/1.5037790

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