Although much heavier than electrons, light nuclei, mainly hydrogen, exhibit Nuclear Quantum Effects (NQE), such as tunnelling and zero-point energy, that can have a large impact on the structure and the dynamics of materials. The standard method to account for them when simulating the static properties at equilibrium is the use of path integrals. However, this method considerably increases the number of degrees of freedom (DOF) with a consequent increase of the parameter space to study. We therefore need to reduce the number of sampling points to avoid too long computation time. To do so, we use the nested sampling method, which reduces a multi-dimensional problem into a one-dimensional integral. Furthermore, the recognition via machine learning methods of cluster structures of the sampling points allows to focus on specific regions that mostly contribute to the energy landscape. Hence, in this Ph.D., we aim to add new search methods for sampling points, new clustering algorithms and eventually integrate neural network methods to nested_fit (a program implementing Nested Sampling). These new computational methods will allow us to study NQE on rather complex systems with many (̣~100) DOF. Finally, we plan to reduce the number of DOF by using principal components analysis and recent algorithms, such as the “greedy” type approaches.

PhD student: Lune MAILLARD

PhD supervisors: Martino TRASSINELLI (Supervisor), Fabio FINOCCHI (Co-supervisor), Julien SALOMON (Coordinator/Adviser)

Research laboratory: Institut des NanoSciences de Paris (INSP)