Nonadiabatic Instanton Rate Theory: A Bridge between Born-Oppenheimer and Fermi's Golden Rule
EMBARGOED UNTIL 2026-12-07
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2023
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Doctoral Thesis
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EMBARGOED UNTIL 2026-12-07
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Abstract
The understanding of chemical reactions is crucial to many aspects of chemistry, biology and physics from photosynthesis to nuclear fusion in stars. Depending on the nature of the reaction, the Born-Oppenheimer approximation may be valid and the reaction is well described as taking place on a single effective potential energy surface. However, the opposite can also be true when the reaction adheres to Fermi's golden rule and a coupled reactant and product potential energy surface is appropriate. For both of these limits successful instanton rate theories exist. The method of steepest descent, which is the key instrument of any instanton rate theory, gives access to the instanton, the optimal tunnelling pathway, which captures nuclear quantum effects such as zero-point energy and nuclear tunnelling at the cost of a classical calculation. In addition, instanton theory is rigorously derived, and it not only predicts reaction rates but also reaction mechanisms.4
% Depending on the nature of the reaction, it may be more suitable to use a definition based on the nuclear configuration i. e. it is the key property transforming upon reaction.
Many chemical reactions do not match either the conditions of the Born-Oppenheimer or the golden-rule limit and they are therefore “nonadiabatic''. The prediction of nonadiabatic rates is one of the largest open challenges in the field of quantum dynamics. This thesis aims to bridge the gap between the Born-Oppenheimer and golden-rule limit via the development and implementation of two nonadiabatic instanton rate theories. The ‘’nonadiabatic ImF theory'' developed in this thesis is a correction to an existing, ad hoc attempt at bridging between the two limits. This correction overcomes the limitations of previous theories in that it predicts rates well in both limits as well as in between, and it was applied to a range of asymmetric multi-dimensional systems. Its utility is however restricted since it cannot describe rates in the limit of strong friction, and its derivation is not rigorous.
A generalised nonadiabatic rate theory was therefore developed which is a true bridging theory between the two extremes. It recovers the definition of reactant and product and the reaction rates in the two limits, while it also approximates the quantum-mechanically exact rates well for the systems studied. In addition, it offers intuitive quantitative and qualitative measures of adiabaticity. While this thesis contains a proof-of-principle study, the theory is immediately applicable to asymmetric problems and a multi-dimensional extension is possible.
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ETH Zurich
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instanton rate theory; Chemical reaction; quantum rate theory; rate theory; nonadiabatic dynamics; semiclassical; Quantum tunnelling; Nonadiabatic
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09602 - Richardson, Jeremy / Richardson, Jeremy
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