{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99490"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99490","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Diagrammatic theories for the vibrational many-body problem","abstract":"Anharmonic vibrational many-body methods are developed for and applied to small molecules and extended systems in a bound potential energy surface (PES). Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies, the latter through the equation-of-motion (EOM) formalism, is defined for an $n$th-order Taylor-series PES. Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman--Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC are derived and implemented with the aid of computer algebra. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation,producing algorithms with optimal cost scaling. A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. An extended STEOM-XVCC (Ext-STEOM-XVCC) method is defined as an $m$th order configuration interaction method with the doubly similarity-transformed Hamiltonian including up to $m$th-order excitation operators. Because the doubly transformed Hamiltonian is dressed with higher-order anharmonic effects, the frequencies of overtones and combinations obtained are different and superior to the corresponding EOM-XVCC method. We compare and contrast the Ext-STEOM-XVCC method to its electronic counterpart. We apply the previously established second-order size-extensive vibrational many-body perturbation (XVMP2) method to the anharmonic phonon dispersion curves of a model two-mass system and the optical phonons of polyethylene. We obtain accurate results despite the presence of multiple Fermi-resonances in the crystalline systems.","abstract_html":"Anharmonic vibrational many-body methods are developed for and applied to small molecules and extended systems in a bound potential energy surface (PES). Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies, the latter through the equation-of-motion (EOM) formalism, is defined for an $n$th-order Taylor-series PES. Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman--Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC are derived and implemented with the aid of computer algebra. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation,producing algorithms with optimal cost scaling. A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. An extended STEOM-XVCC (Ext-STEOM-XVCC) method is defined as an $m$th order configuration interaction method with the doubly similarity-transformed Hamiltonian including up to $m$th-order excitation operators. Because the doubly transformed Hamiltonian is dressed with higher-order anharmonic effects, the frequencies of overtones and combinations obtained are different and superior to the corresponding EOM-XVCC method. We compare and contrast the Ext-STEOM-XVCC method to its electronic counterpart. We apply the previously established second-order size-extensive vibrational many-body perturbation (XVMP2) method to the anharmonic phonon dispersion curves of a model two-mass system and the optical phonons of polyethylene. We obtain accurate results despite the presence of multiple Fermi-resonances in the crystalline systems.","abstract_has_math":true,"creators":["Faucheaux, Jacob A."],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Chemistry","degree_department":null,"school":null,"contributors":["Hirata, So","Gruebele, Martin","Makri, Nancy","Wagner, Lucas"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T17:32:22Z","date_published":"2018-03-13T17:32:22Z","updated_at":"2026-07-22T22:24:37Z","subjects":["Coupled-cluster","Vibrational structure","Anharmonic","Diagrams"],"languages":["en"],"rights":["Copyright 2017 Jacob Faucheaux"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99490","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hirata, So","Gruebele, Martin","Makri, Nancy","Wagner, Lucas"]},{"key":"dc:creator","label":"Author","values":["Faucheaux, Jacob A."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T17:32:22Z","2020-03-14T09:15:22Z","2017-11-28","2017-12"]},{"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":["Coupled-cluster","Vibrational structure","Anharmonic","Diagrams"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Jacob Faucheaux"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99490"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Anharmonic vibrational many-body methods are developed for and applied to small molecules and extended systems in a bound potential energy surface (PES). Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies, the latter through the equation-of-motion (EOM) formalism, is defined for an $n$th-order Taylor-series PES. Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman--Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC are derived and implemented with the aid of computer algebra. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation,producing algorithms with optimal cost scaling. A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. An extended STEOM-XVCC (Ext-STEOM-XVCC) method is defined as an $m$th order configuration interaction method with the doubly similarity-transformed Hamiltonian including up to $m$th-order excitation operators. Because the doubly transformed Hamiltonian is dressed with higher-order anharmonic effects, the frequencies of overtones and combinations obtained are different and superior to the corresponding EOM-XVCC method. We compare and contrast the Ext-STEOM-XVCC method to its electronic counterpart. We apply the previously established second-order size-extensive vibrational many-body perturbation (XVMP2) method to the anharmonic phonon dispersion curves of a model two-mass system and the optical phonons of polyethylene. We obtain accurate results despite the presence of multiple Fermi-resonances in the crystalline systems.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-12-01","The student, Jacob Faucheaux, accepted the attached license on 2017-11-28 at 12:13.","The student, Jacob Faucheaux, submitted this Dissertation for approval on 2017-11-28 at 12:25.","This Dissertation was approved for publication on 2017-11-28 at 16:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11767 on 2018-03-13 at 10:33:41","Made available in DSpace on 2018-03-13T17:32:22Z (GMT). No. of bitstreams: 3 FAUCHEAUX-DISSERTATION-2017.pdf: 1251270 bytes, checksum: b8534414bcb8fc8ab8909751933f6620 (MD5) LICENSE.txt: 4212 bytes, checksum: a301b4344332a044c52dde2fb6598e53 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: 5e2790d78c87e5a08c4fd9dd11dcdbb2 (MD5) Previous issue date: 2017-11-28","Embargo set by: Seth Robbins for item 105458 Lift date: 2020-03-13T17:32:30Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 105458 Lift date: 2020-03-13T17:36:05Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 105458 on 2020-03-14T09:15:22Z."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Diagrammatic theories for the vibrational many-body problem"]}]}],"canonical_facts":{"dc:contributor":["Hirata, So","Gruebele, Martin","Makri, Nancy","Wagner, Lucas"],"dc:creator":["Faucheaux, Jacob A."],"dc:date":["2018-03-13T17:32:22Z","2020-03-14T09:15:22Z","2017-11-28","2017-12"],"dc:description":["Anharmonic vibrational many-body methods are developed for and applied to small molecules and extended systems in a bound potential energy surface (PES). Diagrammatically size-consistent and basis-set-free vibrational coupled-cluster (XVCC) theory for both zero-point energies and transition frequencies, the latter through the equation-of-motion (EOM) formalism, is defined for an $n$th-order Taylor-series PES. Quantum-field-theoretical tools (the rules of normal-ordered second quantization and Feynman--Goldstone diagrams) for deriving their working equations are established. The equations of XVCC and EOM-XVCC are derived and implemented with the aid of computer algebra. Algorithm optimizations known as strength reduction, intermediate reuse, and factorization are carried out before code generation,producing algorithms with optimal cost scaling. A similarity-transformed equation-of-motion vibrational coupled-cluster (STEOM-XVCC) method is introduced as a one-mode theory with an effective vibrational Hamiltonian, which is similarity transformed twice so that its lower-order operators are dressed with higher-order anharmonic effects. From diagonalization of this doubly similarity-transformed Hamiltonian in the small one-mode excitation space, the method simultaneously computes accurate anharmonic vibrational frequencies of all fundamentals, which have unique significance in vibrational analyses. We establish a diagrammatic method of deriving the working equations of STEOM-XVCC and prove their connectedness and thus size-consistency as well as the exact equality of its frequencies with the corresponding roots of EOM-XVCC. An extended STEOM-XVCC (Ext-STEOM-XVCC) method is defined as an $m$th order configuration interaction method with the doubly similarity-transformed Hamiltonian including up to $m$th-order excitation operators. Because the doubly transformed Hamiltonian is dressed with higher-order anharmonic effects, the frequencies of overtones and combinations obtained are different and superior to the corresponding EOM-XVCC method. We compare and contrast the Ext-STEOM-XVCC method to its electronic counterpart. We apply the previously established second-order size-extensive vibrational many-body perturbation (XVMP2) method to the anharmonic phonon dispersion curves of a model two-mass system and the optical phonons of polyethylene. We obtain accurate results despite the presence of multiple Fermi-resonances in the crystalline systems.","Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2019-12-01","The student, Jacob Faucheaux, accepted the attached license on 2017-11-28 at 12:13.","The student, Jacob Faucheaux, submitted this Dissertation for approval on 2017-11-28 at 12:25.","This Dissertation was approved for publication on 2017-11-28 at 16:53.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11767 on 2018-03-13 at 10:33:41","Made available in DSpace on 2018-03-13T17:32:22Z (GMT). No. of bitstreams: 3 FAUCHEAUX-DISSERTATION-2017.pdf: 1251270 bytes, checksum: b8534414bcb8fc8ab8909751933f6620 (MD5) LICENSE.txt: 4212 bytes, checksum: a301b4344332a044c52dde2fb6598e53 (MD5) PROQUEST_LICENSE.txt: 4558 bytes, checksum: 5e2790d78c87e5a08c4fd9dd11dcdbb2 (MD5) Previous issue date: 2017-11-28","Embargo set by: Seth Robbins for item 105458 Lift date: 2020-03-13T17:32:30Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Embargo set by: Seth Robbins for item 105458 Lift date: 2020-03-13T17:36:05Z Reason: Author requested closed access (OA after 2yrs) in Vireo ETD system","Limited Restriction Lifted for Item 105458 on 2020-03-14T09:15:22Z."],"dc:format":["application/pdf"],"dc:identifier":["http://hdl.handle.net/2142/99490"],"dc:language":["en"],"dc:rights":["Copyright 2017 Jacob Faucheaux"],"dc:subject":["Coupled-cluster","Vibrational structure","Anharmonic","Diagrams"],"dc:title":["Diagrammatic theories for the vibrational many-body problem"],"dc:type":["text"],"thesis:degree_discipline":["Chemistry"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:37Z"}