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Generalized Kohn–Sham iteration on Banach spaces

MPS-Authors
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Penz,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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Ruggenthaler,  M.
Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society;

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1.5037790.pdf
(Publisher version), 372KB

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Citation

Laestadius, A., Penz, M., Tellgren, E. I., Ruggenthaler, M., Kvaal, S., & Helgaker, T. (2018). Generalized Kohn–Sham iteration on Banach spaces. The Journal of Chemical Physics, 149(16): 164103. doi:10.1063/1.5037790.


Cite as: http://hdl.handle.net/21.11116/0000-0002-46F5-B
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.