Path Integral Methods in Quantum Rate Theories
dc.contributor.author
Thapa, Manish Jung
dc.contributor.supervisor
Richardson, Jeremy
dc.contributor.supervisor
Hünenberger, Philippe H.
dc.contributor.supervisor
Vanicek, Jiri
dc.date.accessioned
2021-01-11T05:34:28Z
dc.date.available
2021-01-10T17:53:15Z
dc.date.available
2021-01-11T05:34:28Z
dc.date.issued
2020-10-26
dc.identifier.uri
http://hdl.handle.net/20.500.11850/460900
dc.identifier.doi
10.3929/ethz-b-000460900
dc.description.abstract
In this thesis, we propose path integral approaches to include nuclear quantum effects
such as tunneling, delocalization and zero point energy in a chemical simulation. Our
methods exhibit a strong connection to semiclassical instanton (SCI) theory, which
has been rigorously derived from first principles. SCI theory relies on computing the
quantum mechanical rate constant by making a steepest-descent approximation for
the quantum Boltzmann operator. However, our methods go beyond the semiclassical
approximation, and evaluate this operator exactly by sampling over instanton-like
paths and other paths in its vicinity. This allows us to treat systems with strong
anharmonicity where zero-frequency modes cause higher-order quantum fluctuations
to dominate the reaction rates.
We present a set of methods to treat reactions characterized by asymmetric barriers
at high and low temperatures for a challenging set of system parameters. Two of the
methods are inspired by quantum transition-state theories, and include constraint
functions in their formulations to enforce sampling of dominant tunneling paths. The
final approach relies on evaluating the rate constant by the method of saddle-point
approximation along the time variable. All these methods can be evaluated using
path integral Monte Carlo or molecular dynamics techniques, and applied to compute
the reaction rates in complex systems.
Our approach to treat chemical reactions in the nonadiabatic limit has the correct
classical limit, and is exact for a system of many crossed linear potentials. The
method is tested on a wide variety of model systems, and predicts excellent rates
even deep in the tunneling regime. A particularly appealing feature of this approach
is that it is able to accurately describe the inverted regime of the spin-boson model
without resorting to numerical extrapolation techniques. The method has also been
applied by coworkers to study electron-transfer reactions in the aqueous ferrous-ferric
system, where its spin-boson nature was confirmed in the classical limit. Likewise,
our methods developed to treat reactions in the Born-Oppenheimer regime show a
similar level of accuracy in predicting rates where nuclear quantum effects are seen to
play a significant role. We show that, for example, our quantum instanton approach
outperforms SCI theory in computing accurate rates for an asymmetric Eckart barrier.
In presenting the theory and results for these methods, we also demonstrate that some
of the other well-established methods that rely on the saddle-point approximation to
evaluate the time correlation function break down in certain important regimes of
chemical reactions. The deficiencies in these methods are explained and contrasted
against our approaches.
en_US
dc.format
application/pdf
en_US
dc.language.iso
en
en_US
dc.publisher
ETH Zurich
en_US
dc.rights.uri
http://rightsstatements.org/page/InC-NC/1.0/
dc.title
Path Integral Methods in Quantum Rate Theories
en_US
dc.type
Doctoral Thesis
dc.rights.license
In Copyright - Non-Commercial Use Permitted
dc.date.published
2021-01-11
ethz.size
164 p.
en_US
ethz.code.ddc
DDC - DDC::5 - Science::540 - Chemistry
en_US
ethz.identifier.diss
27036
en_US
ethz.publication.place
Zurich
en_US
ethz.publication.status
published
en_US
ethz.leitzahl
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02020 - Dep. Chemie und Angewandte Biowiss. / Dep. of Chemistry and Applied Biosc.::02543 - Inst. f. Molekulare Physikalische Wiss. / Institute of Molecular Physical Science::09602 - Richardson, Jeremy / Richardson, Jeremy
en_US
ethz.leitzahl.certified
ETH Zürich::00002 - ETH Zürich::00012 - Lehre und Forschung::00007 - Departemente::02020 - Dep. Chemie und Angewandte Biowiss. / Dep. of Chemistry and Applied Biosc.::02543 - Inst. f. Molekulare Physikalische Wiss. / Institute of Molecular Physical Science::09602 - Richardson, Jeremy / Richardson, Jeremy
en_US
ethz.date.deposited
2021-01-10T17:53:23Z
ethz.source
FORM
ethz.eth
yes
en_US
ethz.availability
Open access
en_US
ethz.rosetta.installDate
2021-01-11T05:34:50Z
ethz.rosetta.lastUpdated
2024-02-02T12:48:22Z
ethz.rosetta.versionExported
true
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Doctoral Thesis [30085]