2 Internships : Molecular Simulation – Ecole des Ponts ParisTech and Inria Paris

Validity range of implicit solvent models for molecular simulation

This internship lays in the perspective of the newly funded EMC2 multidisciplinary ERC Synergy project on molecular simulation (Sept. 2019-Aug. 2025).

This project gathers 16 permanent researchers from Ecole des Ponts ParisTech, Inria Paris and Sorbonne University, and 12 French and international collaborators.

Molecular simulation has become an instrumental tool in chemistry, condensed matter physics, molecular biology, materials science, and nanosciences. The importance of molec- ular simulation in today’s science was acknowledged by the 1998 and 2013 Nobel prizes in Chemistry. It is also a source of very exciting mathematical and numerical problems.

Implicit solvent models (ISM) are extremely used in molecular simulation. They are currently unavoidable in most quantum chemistry simulations in the liquid phase, where most chemical and biological phenomena take place. ISM are reduced models in which all the solvent molecules surrounding the solute are replaced by a homogeneous dielectric medium, which is much easier to handle numerically.

The purpose of this internship is on the one hand to study whether implicit solvent models can be interpreted in the framework on the general purpose Mori-Zwanzig model reduction method, and on the other hand to test numerically the range of validity of implicit solvation models by comparing them to reference all-atom simulations. Machine learning algorithms will be used to optimize the parameters of the ISM to find the set of parameters which best reproduced the all-atom simulations.

Keywords: numerical simulation of Hamiltonian systems and stochastic differential equa- tions, Mori-Zwanzig model reduction method, machine learning

Collaborations: collaboration with the chemistry department of the University of Pisa (two-week visit in Pisa during the internship)

Requested background: requested background: numerical analysis, proficiency in Python Location: Ecole des Ponts-ParisTech, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée,

France (access: RER A, Noisy-Champs, 25’ from Paris Center)
Gratification: about 500 euros per month
Contacts: Eric Cancès (eric.cances_at_enpc.fr) and Tony Lelièvre (tony.lelievre_at_enpc.fr)


Model reduction in quantum mechanics

This internship lays in the perspective of the newly funded EMC2 multidisciplinary ERC Synergy project on molecular simulation (Sept. 2019-Aug. 2025).

This project gathers 16 permanent researchers from Ecole des Ponts ParisTech, Inria Paris and Sorbonne University, and 12 French and international collaborators.

Molecular simulation has become an instrumental tool in chemistry, condensed matter physics, molecular biology, materials science, and nanosciences. The importance of molec- ular simulation in today’s science was acknowledged by the 1998 and 2013 Nobel prizes in Chemistry. It is also a source of very exciting mathematical and numerical problems.

The fundamental equation in molecular equation is the Schrödinger equation governing the dynamics of the atomic nuclei and electrons composing the molecular system of interest. This model is extremely accurate, but much too complicated to be fully solved numerically. Fortunately, as in many quantum problems, the phenomena of interest take place in a small energy window: this is the case in chemistry (valence electrons are very much affected by chemical reactions, while core electron states are barely modified), as well as in materials science (electronic conductivity in metals is mainly due to the transport of electrons with energy close to the so-called Fermi energy). The purpose of this internship is to study with full mathematical rigor the reduction process consisting in replacing a reference quantum model with an extended energy range with a reduced model focusing on the energy window of interest. Three systems will be considered: a model one-dimensional quantum system for which most calculations are explicit, a small molecule and, if time allows, a 2D material such as graphene.

Keywords: spectral theory of self-adjoint operators, partial differential equations (PDEs), numerical simulation of PDEs

Collaborations: mathematics department of the University of Kansas, physics depart- ment of Harvard University (two-week visit in the US during the internship)

Requested background: functional analysis and partial differential equations, basics of spectral theory, proficiency in Python, Matlab, or Julia

Location: Ecole des Ponts-ParisTech, 6 & 8 avenue Blaise Pascal, 77455 Marne-la-Vallée, France (access: RER A, Noisy-Champs, 25’ from Paris Center)

Gratification: about 500 euros per month
Contacts: Eric Cancès(eric.cances_at_enpc.fr) and Antoine Levitt (antoine.levitt_at_inria.fr)