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Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability

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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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Citation

Laestadius, A., Tellgren, E. I., Penz, M., Ruggenthaler, M., Kvaal, S., & Helgaker, T. (2019). Kohn–Sham Theory with Paramagnetic Currents: Compatibility and Functional Differentiability. Journal of Chemical Theory and Computation, 15(7), 4003-4020. doi:10.1021/acs.jctc.9b00141.


Cite as: http://hdl.handle.net/21.11116/0000-0004-693B-5
Abstract
Recent work has established Moreau–Yosida regularization as a mathematical tool to achieve rigorous functional differentiability in density-functional theory. In this article, we extend this tool to paramagnetic current-density-functional theory, the most common density-functional framework for magnetic field effects. The extension includes a well-defined Kohn–Sham iteration scheme with a partial convergence result. To this end, we rely on a formulation of Moreau–Yosida regularization for reflexive and strictly convex function spaces. The optimal Lp-characterization of the paramagnetic current density L1 ∩ L3/2 is derived from the N-representability conditions. A crucial prerequisite for the convex formulation of paramagnetic current-density-functional theory, termed compatibility between function spaces for the particle density and the current density, is pointed out and analyzed. Several results about compatible function spaces are given, including their recursive construction. The regularized, exact functionals are calculated numerically for a Kohn–Sham iteration on a quantum ring, illustrating their performance for different regularization parameters.