Emmanuel FROMAGER

Professor

✉️ fromagere[at]unistra.fr

Teaching

STUDENTS AND POSTDOC FELLOWS: Wafa MAKHLOUF (PhD), Lucien DUPUY (Postdoctoral Researcher)

Complete list of my publications: .docx (with links to the papers) or .pdf

Research Topics

Ensemble density functional theory of electronic excitations 

Standard density functional theory (DFT) is a pure-ground-state electronic structure theory [1]. It can be extended, in principle exactly, to both neutral and charged excited states via the so-called extended N-centered ensemble formalism [2,3], where the basic variable is a weighted sum of ground- and excited-state electronic densities. The ensemble Hartree-exchange-correlation (Hxc) density functional (from which the electronic repulsion energy in both ground and excited states can be evaluated [4]) varies with the ensemble weights. This weight dependence, whose modelling is still highly challenging, plays a central role in the description of the discontinuities that the Hxc density-functional derivative (the so-called Hxc potential) exhibits when an electronic excitation occurs. This fundamental feature is directly related to the exactification of Koopmans’ theorem in DFT [5,6].     

Quantum embedding theory of strongly correlated electrons

Density matrix embedding theory (DMET) [1,2] is a quantum embedding electronic structure theory where the locality of strong electron correlation is exploited. In DMET, the (extended or molecular) system under study is fragmented. A localised orbital basis is used for that purpose. Each fragment, which can be seen as an open quantum subsystem (because of the entanglement with its environment), is then embedded into a quantum bath which consists of orbitals (as many as in the fragment) that are delocalised over the fragment’s environment. The Schrödinger equation is then solved for the closed and reduced-in-size fragment+bath system (the so-called embedding cluster) from which the properties of the fragment can be deduced. While the procedure is exact for noninteracting (or mean-field) electrons [3], it is still unclear how to optimally construct a systematically improvable embedding for interacting electrons, ideally from an in-principle exact formulation of the theory. For that purpose, connections with density functional theory [4], one-electron reduced density matrix functional theory [3] , as well as quantum information theory are currently explored, for example.