Séminaires à venir

In principle, all properties of the quantum state of a molecule or material can be deduced from its wavefunction representation. In practice, obtaining the latter by solving its Schrödinger equation is prohibitively expensive for all but the simplest of systems. Several reasons contribute to this, the most obvious being the sheer size of the wavefunction’s domain. Indeed, as the electronic wavefunction depends on all their -positions individually, the size of its grid representation, aiming for an (optimistic) estimate of 10 grid points per degrees of freedom, shoots to wavefunction values to compute and store for an -electron system. This “exponential wall” renders the mere storage of a wavefunction representation very costly, let alone computing it in the first place. It illustrates the need for a reduced representation that we can compute, store, and from which physical observables can be extracted. Such is the purpose of Density Functional Theory (DFT), establishing a one-to-one correspondence between properties of the ground electronic state and its density without distinction of individual electrons. Its unparalleled balance between cost and accuracy has shaped the fields of chemistry and condensed matter, allowing to treat systems with up to thousands of atoms. The situation is different when one turns to excited electronic states populated upon absorption of a photon, and thus crucial to describe light-induced reactivity. Their computation by the Time-Dependent extension of DFT, typically used in the Linear Response regime (LR-TDDFT), does not achieve the broad applicability of its parent ground-state approach because of lackluster accuracy in several situations. Part of these limitations stems from the Born-Oppenheimer (BO) approximation, treating nuclei as classical point-charges whose distribution parameterizes the electronic Hamiltonian. This BO separation between electrons and nuclei, while being computationally advantageous and most often very accurate for molecular dynamics in the ground electronic state, fails spectacularly in the vicinity of degeneracies between states called conical intersections (CI), which provide the dominant pathways for fast relaxation of molecules after light absorption. Around CIs, the slightest change to nuclear positions induces a drastic change in the character of BO electronic states, so that the (modest) spatial extension of nuclei induced by their quantum nature brings important electro-nuclear correlation effects. In this talk, I will present an extension of DFT beyond the BO picture [1]. Incorporating nuclear quantum effects and electro-nuclear correlation leads to a molecular DFT, where all properties of the system are dependent on not only an effective electronic density, but also a nuclear density. I will introduce the exact theory, discuss practical ways to “recycle” functionals from the parent ground-state DFT, and present our recent reformulation of molecular DFT using Exact Factorization [2] to derive coupled effective electronic and nuclear equations. [1] Fromager & Lasorne, Electron. Struct. 6 025002 (2024) [2] Dupuy, Lasorne & Fromager, arXiv:2601.03972