**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].

- [1] Andrew M. Teale, Trygve Helgaker, Andreas Savin, …, E. Fromager, et al., Phys. Chem. Chem. Phys. (2022) 24, 28700-28781.
- [2] F. Cernatic, P.-F. Loos, B. Senjean, and E. Fromager, Phys. Rev. B 109, 235113 (2024).
- [3] F. Cernatic and E. Fromager, J Comput Chem. 2024, 45:1945–1962.
- [4] E. Fromager, Phys. Rev. Lett. 124, 243001 (2020).
- [5] F. Cernatic, B. Senjean, V. Robert, and E. Fromager, Top Curr Chem (Z) 380, 4 (2022).
- [6] M. J. P. Hodgson, J. Wetherell, and E. Fromager, Phys. Rev. A 103, 012806 (2021).

**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.

- [1] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012).
- [2] S. Wouters, C. A. Jiménez-Hoyos, Q. Sun, and G. K.-L. Chan, J. Chem. Theory Comput. 12, 2706 (2016).
- [3] S. Sekaran, O. Bindech, and E. Fromager, J. Chem. Phys. 159, 034107 (2023).
- [4] S. Sekaran, M. Saubanère, and E. Fromager, Computation 2022, 10, 45.