At the Interface of Mathematics and Chemistry: Modelling Metastable Anions
Supervisor: Dr Cate Anstoter
School: Chemistry
Description:
Metastable electronic states play a central role in electron- and photon-driven chemistry. Whenever a molecule temporarily captures an electron or absorbs high-energy radiation, it can enter a short-lived anionic state that either relaxes, fragments, or ejects the extra electron. These processes underpin radiation damage, plasma chemistry, atmospheric chemistry, and many catalytic cycles. They are especially critical in astrochemical environments such as the interstellar medium, planetary atmospheres, and cometary comae, where intense electron and photon bombardment occurs in the absence of a stabilising solvent. Astrochemistry has long recognised that ion-driven chemistry shapes molecular evolution in space; however, theoretical and experimental attention has focused disproportionately on cations. Anions are far less studied, largely because their key reactive intermediates are metastable and difficult to characterise. Consequently, we are currently missing half of the redox landscape in space chemistry.
The difficulty arises because metastable anionic states are not truly bound. They possess finite lifetimes and are intrinsically susceptible to autodetachment of the excess electron. Experimentally, this makes them challenging to isolate and probe. Theoretically, they fall outside the conventional Hermitian framework that underpins most quantum chemistry. Standard electronic structure methods are designed for bound states with real-valued energies. In contrast, metastable states must be described as resonances, characterised by complex energies whose imaginary component encodes the lifetime. This requires mathematical machinery (such as non-Hermitian quantum mechanics, complex scaling, or related techniques) that lies beyond the standard toolkit of many chemists. Developing and implementing such methods demands fluency in both advanced mathematics and theoretical chemistry, making this an ideal project at the interface of the two disciplines.
Why revisit this problem now? Many of the seminal theoretical approaches to electronic resonances were developed over thirty years ago, when computational resources severely limited their applicability. These methods were often benchmarked on small atomic or diatomic systems and may not transfer reliably to larger, chemically relevant molecular anions. Today, vastly increased computational power, improved numerical algorithms, and modern mathematical insights create an opportunity to reassess and improve how metastable states are modelled. This project will evaluate existing resonance methodologies, test their robustness for molecular anions, and explore improved strategies for predicting lifetimes and decay pathways. By refining how we describe metastable anions, we aim to unlock a largely inaccessible sector of redox chemistry and provide new theoretical tools for understanding electron-driven processes in chemistry and space.