Mathematical approach to N -centered ensemble DFT and associated methods for the study of open systems
Guillaume Grente, Zakaria Belhachmi · HAL (Le Centre pour la Communication Scientifique Directe) · 2023
A fundamental aspect of the study of N-electronic systems is to obtain information on the statesin which these systems have minimal energy. In practice a numericalsearch of such states is impossible to carry out, so that alternativeapproaches have been developed, the one around which this work revolvesbeing to consider electronic systems through their electronic densityrather than their state. A first implementation of this idea was proposed by Thomas and Fermi and was later revisited by Hohenberg and Kohn who set the basis for the method known today as Density Functional Theory (DFT)for which an in-depth mathematical study has been established by Lieb.Since then, the ideas leadingto the construction of DFT have been adapted to the context of electronicsystems with a fractional number of electrons (open systems), firstthrough PPLB DFT and more recently through the definitionof N-centered ensemble DFT. In both casesit is unclear whether the mathematical properties established forregular DFT can be expected to hold true despite a growing use by quantum chemistry community and physicists. This question is the mainproblematic of our work, in which we shall study the analogy betweenN-centered ensemble and regular DFT, from their construction to the methodsthat are derived from them. This will lead us to construct a Kohn-Shamscheme for N-centered ensemble DFT. We also investigate the links between this theory and optimal transport formulation of DFT-like functionals and finally, we present the Hubbard Dimer calculations framework for N-centered ensemble DFT.