2026-09-19T05:52:27Zhttps://ecommons.cornell.edu/server/oai/requestoai:ecommons.cornell.edu:1813/672612026-05-15T19:45:42Zcom_1813_35col_1813_47
Church, Matthew Steven
Ananth, Nandini
Loring, Roger F.
Ezra, Gregory Sion
2019-10-15T15:28:45Z
2019-10-15T15:28:45Z
2019-05-30
ProQuest Submission ID: 11376
ProQuest Publication ID: 13878728
https://hdl.handle.net/1813/67261
https://doi.org/10.7298/fys0-3128
11050242
Semiclassical (SC) theory offers a pedagogically rich connection between quantum and classical perspectives of nature, and, furthermore, is a promising approach to incorporating quantum effects into molecular dynamics simulations. However, a variety of numerical challenges associated with SC methods, such as the cumbersome search for special trajectories, or the integration of highly oscillatory functions (i.e. the SC ``sign problem"), generally renders SC theory impractical for all but very simple, low-dimensional systems. In this dissertation we derive a variety of mixed quantum-classical (MQC) representations of the real-time correlation function within the SC initial value representation (SC-IVR) using the modified Filinov filtration (MFF) technique. The most promising of these methods are subsequently tested on a number of low- and high-dimensional systems. Each of these methods have three significant advantages. (1) They offer a significant improvement upon the SC-IVR ``sign problem." (2) They offer mode-specific quantization in a dynamically consistent framework. And (3) they are significantly easier to implement than other leading SC-IVR methodologies. The extension of these methods to nonadiabatic systems is made as well. We conclude that, in future studies of a variety of non-equilibrium molecular systems, particularly those that exhibit strong nuclear quantum effects such as interference, the novel SC-IVR methods presented here should prove to be very powerful.
en_US
Quantum Mechanics
Physical chemistry
Computational Chemistry
chemical physics
initial value representation
semiclassical dynamics
theoretical chemistry
Semiclassical Approaches to Complex Chemical Simulation in Real Time
dissertation or thesis
application/pdf
Chemistry and Chemical Biology
Cornell University
Doctor of Philosophy
Ph.D., Chemistry and Chemical Biology
https://hdl.handle.net/1813/59810
Publication
Cornell Theses and Dissertations
Church, Matthew Steven
5893a6ea-7af3-41d7-abc6-04bcd26ab5df
open.access
open.access
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<Abstract>Semiclassical (SC) theory offers a pedagogically rich connection between quantum and classical perspectives of nature, and, furthermore, is a promising approach to incorporating quantum effects into molecular dynamics simulations. However, a variety of numerical challenges associated with SC methods, such as the cumbersome search for special trajectories, or the integration of highly oscillatory functions (i.e. the SC ``sign problem"), generally renders SC theory impractical for all but very simple, low-dimensional systems. In this dissertation we derive a variety of mixed quantum-classical (MQC) representations of the real-time correlation function within the SC initial value representation (SC-IVR) using the modified Filinov filtration (MFF) technique. The most promising of these methods are subsequently tested on a number of low- and high-dimensional systems. Each of these methods have three significant advantages. (1) They offer a significant improvement upon the SC-IVR ``sign problem." (2) They offer mode-specific quantization in a dynamically consistent framework. And (3) they are significantly easier to implement than other leading SC-IVR methodologies. The extension of these methods to nonadiabatic systems is made as well. We conclude that, in future studies of a variety of non-equilibrium molecular systems, particularly those that exhibit strong nuclear quantum effects such as interference, the novel SC-IVR methods presented here should prove to be very powerful.</Abstract>
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