Title
Non-linear optimisation in quantum chemistry
Abstract
A central problem in quantum chemistry is computing the electronic energy levels of a molecule from the Schrodinger equation. Knowledge of these energy levels provides access to the chemical and optical properties of chemical species. To perform this computationally, we must solve large linear or non-linear optimisation problems to identify both minima and higher-index saddle points on an electronic energy landscape. Often, this optimisation is further complicated by invariances in the physical description that must be taken into account. In this talk, I will explore the differential geometry of molecular quantum chemistry and its implications for optimisation in quantum chemistry. I will describe the various manifolds that arise in computational methods and introduce robust techniques to optimise different quantum energy levels using common approximations such as mean-field theory. If time permits, I will extend these concepts to new approximations based on Lie algebras, which are compatible with emerging quantum computation for quantum chemistry.
Bio
Hugh is a specialist in molecular electronic structure theory and currently holds a Royal Society University Research Fellowship in the Department of Chemistry at University College London. His research focuses on developing new theoretical methods to understand and predict molecular properties, particularly addressing the breakdown of electronic structure approximations for open-shell ground and excited states. He has pioneered the energy landscape approach to electronic structure theory and developed new quantum chemistry algorithms to leverage the power of emerging quantum computers. Hugh completed his PhD in Chemistry at University of Cambridge in 2020 under the supervision of Dr Alex Thom and previously held research fellowships at Downing College, Cambridge and New College, Oxford. He currently serves on the Early Career Editorial Advisory Board of the Journal of Chemical Theory and Computation.