Exactification of the one-electron picture beyond regular ground-state density functional theory: An ensemble perspective

by Prof. Emmanuel Fromager (Université de Strasbourg)

Monday 8 Apr 2024, 11:00 → 12:00 Europe/Zurich

Auditorium (WHGA/001)

In this presentation I will briefly review how Kohn-Sham density functional theory (KS-DFT), which has become the workhorse of quantum chemistry and materials science [1], exactifies the simpler but a priori unphysical non-interacting description of electrons (where the electron-electron repulsion is not treated explicitly), that is sometimes referred to as the one-electron picture, because it is equivalent to solving a Schrödinger-like equation for a single electron. How the corresponding one-electron (orbital) energies relate to charged (ionization or affinity) or neutral excitation energies of the true physical (i.e., interacting) electronic system under study has been discussed extensively in the literature in the past decade. In this talk, I will revisit this problem from a different perspective, by introducing the concept of extended N-centered many-electron ensemble [2,3] (see also Refs. 4-7 and the references therein). Within such a formalism I will show that the one-electron picture can be made exact also for the excited states. The price to pay for reaching such an exactification is the well-known and challenging description of density-functional derivative discontinuities. I will show that, in the context of KS-DFT for ensembles, the latter is equivalent to describing the ensemble weight dependence of density functionals. The development of ensemble density-functional approximations will finally be discussed.

References 

[1] A.Teale, ..., E. Fromager, et al., Phys. Chem. Chem. Phys., 2022, 24, 28700-28781.
[2] F. Cernatic, P.-F. Loos, B. Senjean, and E. Fromager (2024), arXiv:2401.04685
[3] F. Cernatic and E. Fromager (2024), arXiv:2402.07161
[4] E. K. U. Gross, L. N. Oliveira, and W. Kohn, Phys. Rev. A 37, 2809 (1988).
[5] F. Cernatic, B. Senjean, V. Robert, and E. Fromager, Top Curr Chem (Z) 380, 4 (2022). 
[6] B. Senjean and E. Fromager, Phys. Rev. A 98, 022513 (2018). 
[7] T. Gould, D. P. Kooi, P. Gori-Giorgi, and S. Pittalis, Phys. Rev. Lett. 130, 106401 (2023).