Herein we propose a 3 years fully funded PhD at the Institut Charles Gerhardt of the university of Montpellier (Mediterranean cost, south of France), supervised by Bruno Senjean (https://scholar.google.fr/citations?user=gTSQ23kAAAAJ&hl=fr, [email protected]) and Matthieu Saubanère (https://www.icgm.fr/en/matthieu-saubanere-en, [email protected]).

We are looking for a highly motivated candidate, with a background of Quantum mechanics, theoretical physics/chemistry and basics in programing (python, fortran).

title: Reduced density-matrix functionals in quantum chemistry

Abstract: More than 50 years ago, numerous chemical and physical properties of molecules and solids have been elucidated through the advent of the density functional theory (DFT), which predictions led to the understanding of many phenomena at the quantum scale, such as in pharmaceutical, catalysis or condensed matter applications.
The efficiency of DFT lies in the choice of the electronic density as the new fundamental variable, instead of the wavefunction. Indeed, the energy and many other properties are easily accessible within the Kohn-Sham formalism via a self-consistent process on an independent electron gas subject to an effective potential. The latter is the so-called exchange-correlation potential Vxc that contains the ion-electron interaction and electron-electron correlation. Unfortunately, neither the shape or the value of Vxc are known exactly, and the more than 50 years of methodological development in the construction of density functionals still lead to non-negligible errors.
In this context, the reduced density matrix functional theory (rDMFT) is more and more regarded as a viable alternative to DFT. With only a small increase in computational cost by replacing the density by the density matrix as the fundamental variable, rDMFT can evaluate the electron-electron interactions much more precisely than with the simple Vxc potential in DFT. Similarly as DFT, the expression of the energy as a functional of the density matrix remains to be determined and is the goal of this thesis project. To do so, we will rely on a quasi-universal behavior of the electron-electron correlation energy with respect to a metric representing the “distance” of the system from the independent electron gas. Such a behavior has already been identified in simple models and needs to be generalized to any chemical system of interest. Hence, the success of this project relies on (i) the generalization of the universal behavior of the correlation energy functional of the density matrix, (ii) the implementation of rDMFT with the new functional of the density matrix in an Open-Source quantum chemistry code (Psi4), (iii) the estimation of the accuracy and the optimization of the algorithm on realistic chemical systems (transition metal complexes for catalysis and oxides for energy storage and energy conversion, for instance).
If successful, this project will lead to a much better description of chemical and physical properties at the quantum scale, and will be beneficial for many scientific communities.