{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/101548"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/101548","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Phase space and path integral approaches to quantum dynamics","abstract":"\"Exact quantum dynamical simulation of processes in highly coupled condensed phase reactions is extremely challenging. The work reported in this dissertation builds on top of two different approaches. First, we present methods for calculating the multidimensional Wigner function. We start with a simple and approximate method which utilizes classical trajectories. This fits well with the subsequent classical propagation involved in a quasiclassical simulation. We use this method to study molecular Hamiltonians in both normal mode and Cartesian coordinates. Despite the simplicity of this method, there can be systems which are extremely anharmonic, where the method can be extremely slow to converge when there is no obviously good starting point. To overcome this problem, we propose a numerically exact path integral based method which can be systematically converged to any desired level of accuracy at increasing computational cost. Both these methods can be used with quantum classical simulation frameworks. Second, we present developments of rate theory methods. We extend the existing reactive flux rate methods to exact quantum classical methods. Two different initial conditions are proposed. If the transients are important, we show that the so-called \"\"non-equilibrium\"\" initial condition can help us unify the fast timescales as well as the long timescale dynamics governed by the rate. On the other hand, if the transients are of less importance, we propose a \"\"near equilibrium\"\" initial condition that can very effectively get rid of most of the transients. This initial condition captures the system-solvent interaction without increasing the complexity of the algorithm. Finally, we present a method of incorporating the concept of blip summation into the quantum-classical path integral (QCPI) method. This gives additional speedup on top of all the other advancements that make QCPI a very attractive method for doing exact quantum dynamics in condensed phase.\"","abstract_html":""Exact quantum dynamical simulation of processes in highly coupled condensed phase reactions is extremely challenging. The work reported in this dissertation builds on top of two different approaches. First, we present methods for calculating the multidimensional Wigner function. We start with a simple and approximate method which utilizes classical trajectories. This fits well with the subsequent classical propagation involved in a quasiclassical simulation. We use this method to study molecular Hamiltonians in both normal mode and Cartesian coordinates. Despite the simplicity of this method, there can be systems which are extremely anharmonic, where the method can be extremely slow to converge when there is no obviously good starting point. To overcome this problem, we propose a numerically exact path integral based method which can be systematically converged to any desired level of accuracy at increasing computational cost. Both these methods can be used with quantum classical simulation frameworks. Second, we present developments of rate theory methods. We extend the existing reactive flux rate methods to exact quantum classical methods. Two different initial conditions are proposed. If the transients are important, we show that the so-called ""non-equilibrium"" initial condition can help us unify the fast timescales as well as the long timescale dynamics governed by the rate. On the other hand, if the transients are of less importance, we propose a ""near equilibrium"" initial condition that can very effectively get rid of most of the transients. This initial condition captures the system-solvent interaction without increasing the complexity of the algorithm. Finally, we present a method of incorporating the concept of blip summation into the quantum-classical path integral (QCPI) method. This gives additional speedup on top of all the other advancements that make QCPI a very attractive method for doing exact quantum dynamics in condensed phase."","abstract_has_math":false,"creators":["Bose, Amartya"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemistry","degree_department":null,"school":null,"contributors":["Makri, Nancy","Wagner, Lucas","Gruebele, Martin","Hirata, So"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-09-27T16:17:45Z","date_published":"2018-09-27T16:17:45Z","updated_at":"2026-07-22T22:24:40Z","subjects":["quantum dynamics, path integrals, wigner distributions, rate"],"languages":["en"],"rights":["Copyright 2018 Amartya Bose"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/101548","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Makri, Nancy","Wagner, Lucas","Gruebele, Martin","Hirata, So"]},{"key":"dc:creator","label":"Author","values":["Bose, Amartya"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-09-27T16:17:45Z","2018-07-10","2018-08"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Chemistry"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["quantum dynamics, path integrals, wigner distributions, rate"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2018 Amartya Bose"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/101548"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"Exact quantum dynamical simulation of processes in highly coupled condensed phase reactions is extremely challenging. The work reported in this dissertation builds on top of two different approaches. First, we present methods for calculating the multidimensional Wigner function. We start with a simple and approximate method which utilizes classical trajectories. This fits well with the subsequent classical propagation involved in a quasiclassical simulation. We use this method to study molecular Hamiltonians in both normal mode and Cartesian coordinates. Despite the simplicity of this method, there can be systems which are extremely anharmonic, where the method can be extremely slow to converge when there is no obviously good starting point. To overcome this problem, we propose a numerically exact path integral based method which can be systematically converged to any desired level of accuracy at increasing computational cost. Both these methods can be used with quantum classical simulation frameworks. Second, we present developments of rate theory methods. We extend the existing reactive flux rate methods to exact quantum classical methods. Two different initial conditions are proposed. If the transients are important, we show that the so-called \"\"non-equilibrium\"\" initial condition can help us unify the fast timescales as well as the long timescale dynamics governed by the rate. On the other hand, if the transients are of less importance, we propose a \"\"near equilibrium\"\" initial condition that can very effectively get rid of most of the transients. This initial condition captures the system-solvent interaction without increasing the complexity of the algorithm. Finally, we present a method of incorporating the concept of blip summation into the quantum-classical path integral (QCPI) method. This gives additional speedup on top of all the other advancements that make QCPI a very attractive method for doing exact quantum dynamics in condensed phase.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Amartya Bose, accepted the attached license on 2018-07-09 at 18:18.","The student, Amartya Bose, submitted this Dissertation for approval on 2018-07-09 at 18:18.","This Dissertation was approved for publication on 2018-07-10 at 10:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12785 on 2018-09-27 at 10:47:28","Made available in DSpace on 2018-09-27T16:17:45Z (GMT). No. of bitstreams: 2 BOSE-DISSERTATION-2018.pdf: 1191335 bytes, checksum: d1dde3421a3f418a461a375d523df361 (MD5) LICENSE.txt: 4209 bytes, checksum: e88ef883114267db6afdc0212610cfda (MD5) Previous issue date: 2018-07-10"]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Phase space and path integral approaches to quantum dynamics"]}]}],"canonical_facts":{"dc:contributor":["Makri, Nancy","Wagner, Lucas","Gruebele, Martin","Hirata, So"],"dc:creator":["Bose, Amartya"],"dc:date":["2018-09-27T16:17:45Z","2018-07-10","2018-08"],"dc:description":["\"Exact quantum dynamical simulation of processes in highly coupled condensed phase reactions is extremely challenging. The work reported in this dissertation builds on top of two different approaches. First, we present methods for calculating the multidimensional Wigner function. We start with a simple and approximate method which utilizes classical trajectories. This fits well with the subsequent classical propagation involved in a quasiclassical simulation. We use this method to study molecular Hamiltonians in both normal mode and Cartesian coordinates. Despite the simplicity of this method, there can be systems which are extremely anharmonic, where the method can be extremely slow to converge when there is no obviously good starting point. To overcome this problem, we propose a numerically exact path integral based method which can be systematically converged to any desired level of accuracy at increasing computational cost. Both these methods can be used with quantum classical simulation frameworks. Second, we present developments of rate theory methods. We extend the existing reactive flux rate methods to exact quantum classical methods. Two different initial conditions are proposed. If the transients are important, we show that the so-called \"\"non-equilibrium\"\" initial condition can help us unify the fast timescales as well as the long timescale dynamics governed by the rate. On the other hand, if the transients are of less importance, we propose a \"\"near equilibrium\"\" initial condition that can very effectively get rid of most of the transients. This initial condition captures the system-solvent interaction without increasing the complexity of the algorithm. Finally, we present a method of incorporating the concept of blip summation into the quantum-classical path integral (QCPI) method. This gives additional speedup on top of all the other advancements that make QCPI a very attractive method for doing exact quantum dynamics in condensed phase.\"","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-09-27 without embargo terms","The student, Amartya Bose, accepted the attached license on 2018-07-09 at 18:18.","The student, Amartya Bose, submitted this Dissertation for approval on 2018-07-09 at 18:18.","This Dissertation was approved for publication on 2018-07-10 at 10:56.","DSpace SAF Submission Ingestion Package generated from Vireo submission #12785 on 2018-09-27 at 10:47:28","Made available in DSpace on 2018-09-27T16:17:45Z (GMT). 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