Numerical Analysis of Electronic Structure Methods for Molecules and Materials

• Applicant: Dr. Muhammad Hassan, Ph.D.
• Subject Area: Mathematics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 555300205

This project is concerned with the numerical analysis of cutting-edge electronic structure methods used to study molecules and materials with a particular focus on the coupled cluster method, which involves a system of coupled, non-linear equations. The project builds upon the previously undertaken a priori error analysis of the coupled cluster method for molecular systems and aims to advance the state-of-the-art by developing a posteriori error certification for molecular systems on the one hand, and laying the foundation of an a priori error analysis for crystalline materials on the other hand. For the molecular case, we aim to derive a posteriori error estimators that upper bound different components of the error, namely, the discretisation error and the non-linear solver iteration error. These estimators can then be used to develop adaptive error balancing strategies that seek to obtain an approximate solution of the coupled cluster equations up to a given accuracy using a minimal computational cost. For the crystalline material case where the existing numerical analysis is less mature, we seek to establish well-posedness of the supercell coupled cluster model. To do so, we aim to first perform the numerical analysis of the periodic Hartree-Fock model-- taking inspiration from similar analyses of Kohn-Sham DFT-- and then adapt arguments from the molecular case to study the periodic supercell coupled cluster equations.

• DFG Programme: Emmy Noether Independent Junior Research Groups