Mathematical Methods in Quantum Chemistry

Abstract

Quantum chemistry focuses on modelling and simulating the behaviour of molecular systems using the fundamental principles of quantum mechanics. However, the underlying equations, such as the Schrödinger equation for computing the ground state of $N$ electrons, which is a partial differential equation defined on ${\mathbb{R}}^{3N}$, suffer from the curse of dimensionality. As a result, simulating even moderately sized molecules demands advanced techniques in analysis, approximation and reduced-order modelling for overcoming the naive computational complexity. In this workshop, the rapidly growing mathematical community working in the field together with several quantum chemists and physicists were gathered to discuss recent advances in areas such as (1) the mathematical and numerical analysis of standard models used in the field, including Density Functional Theory, Coupled Cluster, and the Density Matrix Renormalization Group (2) the development of efficient numerical methods, relying e.g. on the development of error bounds and (3) the opportunities of recent data-driven methods towards the approximation of wavefunctions or density matrices.