Dr Tim Hele

Theoretical Chemist

Research Fellow, Jesus College, Cambridge University, UK

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My research examines the quantum mechanical motion and structure of small and light particles such as the atoms and electrons in molecules and how physical properties such as reaction rates and spectra can be calculated for them. The research ranges from mathematical methodological development to applications in large multidimensional systems. Themes include:

Non-adiabatic dynamics

Researching in the Ananth group at Cornell University, I have derived the exact nonadiabatic propagator in the mapping variable representation, writing the result in the Liouvillian formalism. Approximations to this exact result lead to pre-existing methods and their error terms from the exact quantum evolution.

While a master's student with Prof David Manolopoulos FRS, I investigated the computation of thermal reaction rates with a mean field form of non-adiabatic ring polymer molecular dynamics, showing that it was a considerable improvement on rate calculation only on the lower adiabatic surface in one-dimensional models.

More recently, with Matt Church and others I have invented the MInt algorithm, a symplectic propagator for the Meyer-Miller Hamiltonian, which we have then implemented in the mixed quantum-classical initial value representation (MQC-IVR) form of semiclassical dynamics.

Chromophore Design and Singlet Fission

Present research includes the design of intensely absorbent organic chromophores for photovoltaic applications (solar cells). There is a particular focus on singlet fission candidates which have the potential to substantially increase solar cell efficiency, with research on pi-bridge-pi chromophores recently published in the Journal of the American Chemical Society.

This involves high-level electronic structure computation for individual molecules and examining theoretical models to provide general rules for a wide variety of systems.

Quantum Dynamics

Collaborating with the Althorpe group, Michael Willatt, Andrea Muolo, Stuart Althorpe and I derived a form of linearized dynamics which conserves the quantum Boltzmann distribution: Matsubara Dynamics.

We then showed that two popular and successful approximate quantum dynamics methods, Centroid Molecular Dynamics (CMD) and Ring Polymer Molecular Dynamics (RPMD) could be related to Matsubara dynamics, deriving for the first time the explicit error terms between these methods and the exact quantum result.

Researching independently, I then related Thermostatted Ring Polymer Molecular Dynamics (TRPMD) to exact quantum dynamics via Matsubara dynamics, giving the explicit error in the propagator and a dynamical justification for the friction parameter. This research won the 2016 Longuet-Higgins Prize from Molecular Physics.

This research has been summarized in a recent New View article in Molecular Physics which reviews thermal quantum time-correlation functions from classical-like dynamics.

Quantum Transition-State Theory and Rate Theory

Stuart Althorpe and I have derived Quantum Transition-State Theory, the quantum analogue of transition-state theory, which had been claimed not to exist since 1939.

In an international collaboration with Prof Yury Suleimanov (MIT/Cyprus) I applied TRPMD to reaction rate theory, linked it to Kramers theory, and showed that, despite its promise for the computation of spectra, it is generally no more accurate than (unthermostatted) RPMD for the computation of reaction rates.

In a collaboration with Prof Mark Tuckerman and his group at New York University, we applied QTST and RPMD rate theory to diffusion in clathrate hydrates, showing how hydrogen diffuses more slowly that deuterium at intermediate temperates (50K) as the hydrogen molecule "swells" as it passes through the bottleneck between the clathrate cages more than the deuterium molecule. However, at low temperatures (around 8K) the effect is reversed and hydrogen tunnels through the barrier faster than deuterium.

With Stuart Althorpe I have also published an alternative derivation of quantum transition-state theory and, as part of a review article on thermal quantum time-correlation functions, showed how it could be derived in the Matsubara formalism.

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