Mathematical And Numerical Issues in First-principle molecular simulation – MANIF

Molecular simulation based on electronic structure calculation (which is the principal component of computational quantum physics) aims at numerically investigating the physical properties of matter, and has a huge number of applications in the fields of chemistry, condensed matter physics, materials science, molecular biology, and nanosciences.

There is a need to establish a solid expertise in France covering all the mathematical and numerical aspects required in electronic structure computation. Indeed, the commitment of the mathematical community, and in particular the communities of numerical analysis and scientific computing, is clearly not high enough in comparison with the CPU time spent on these problems and the number of applied scientists using these models on a daily basis. The acceptance of this project would greatly contribute to the development of these research themes in France, in particular through the training of young scientists.

The main focus of this proposal is twofold:
1. providing sound mathematical foundations to the most popular models describing electronic excitations in semiconductors (with applications in solar cell technologies for instance), namely the time-dependent density functional theory (TDDFT) and the GW model. This is indeed a mandatory first step to propose dedicated and efficient numerical discretizations for the models at hand;
2. deriving a priori and a posteriori error estimators for the most common models used to describe solids in electronic structure computations, namely the Kohn-Sham models, which consist in minimizing some energy functional under orthonormality constraints and give rise to systems of nonlinear elliptic eigenvalue problems.

Our team consists of two partners: CERMICS (Ecole des Ponts ParisTech) and Laboratoire Jacques-Louis Lions (Université Paris 6). We believe that our team is well-suited to the aims of the proposal since it combines a solid and internationally recognized expertize in the modeling, theoretical understanding and numerical discretization of problems from quantum physics through the partner CERMICS, as well as a world-leading expertise in the numerical analysis of partial differential equations through the partner Laboratoire Jacques-Louis Lions. The relevance of the problems we aim to study is guaranteed by the commitment of several scientists from the applied fields (which appear as external contributors or advisor in some of the tasks), some of them being long-term collaborators of the members of the project.

To conduct this ANR project, we ask for three postdoctoral positions (54 months in total), as well as some additional funding for equipment (computing ressources) and for participations to international conferences. In particular, we plan to use a possible funding by the ANR to favor attendance to events organized by the applied communities (physicists, chemists, materials scientists) in order to advertise our results to the practitioners of the field, and collect information on the lastest developments and trends.