XVIth International Workshop on
Quantum Systems in
Chemistry and Physics
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Functional Derivatives and Differentiability in Density-Functional Theory
Yan Alexander Wang
Department of Chemistry, University of British Columbia, Vancouver, BC V6T 1Z1, Canada
Based on Lindgren and Salomonsonís analysis on Fréchet differentiability [ Phys. Rev. A 67, 056501 (2003)], we showed a specific variational path along which the Fréchet derivative of the Levy-Lieb functional does not exist in the unnormalized density domain. This conclusion still holds even when the density is restricted within a normalized space. Furthermore, we extended our analysis to the Lieb functional and demonstrated that the Lieb functional is not Fréchet differentiable. Along our proposed variational path, the Gâteaux derivative of the Levy-Lieb functional or the Lieb functional takes a different form from the corresponding one along other more conventional variational paths. This fact prompted us to define a new class of unconventional density variations and inspired us to present a modified density variation domain to eliminate the problems associated with such unconventional density variations.


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