High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models
The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivatio...
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| Veröffentlicht in: | Molecular physics Jg. 120; H. 15-16 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Abingdon
Taylor & Francis
18.08.2022
Taylor & Francis Ltd |
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| ISSN: | 0026-8976, 1362-3028 |
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| Abstract | The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2 . . . ), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C
2v
, C
3v
and T
d
molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions. |
|---|---|
| AbstractList | The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2 . . . ), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C
2v
, C
3v
and T
d
molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions. The paper describes methods and fast computational algorithm for building effective Hamiltonians in molecular physics using perturbative approach. Separations of fast and slow variables are considered in the framework of contact transformations (CT). The particular focus is on a systematic derivation of effective models for rovibrational spectroscopy from ab initio-based potential energy surfaces with an exhaustive review of previous studies in this field. We consider applications to several types of polyads coupled by Fermi, Coriolis, Darling-Dennison and other types of resonance interactions with examples for asymmetric top, symmetric top and spherical top molecules. A flexible choice of the modelling operator accounts for strong couplings of various types of nuclear motion in molecules among closely lying levels including vibrational resonance schemes (2:1:2 . . . ), (2:1:2:1), (4:2:6:3), (3:2:1:2:1:1), etc. that occur for C2v, C3v and Td molecules and their isotopic species. The method is implemented in the MOL_CT programme suite, which offers a complementary tool to variational methods in terms of convergence and computational time. The range of applications is also different. The goal of the CT method is providing mathematical models for analyses of molecular spectra with the high-resolution accuracy using physically meaningful parameters derived from ab initio functions. |
| Author | Tyuterev, Vladimir Tashkun, Sergey Rey, Michael Nikitin, Andrei |
| Author_xml | – sequence: 1 givenname: Vladimir orcidid: 0000-0002-2181-1158 surname: Tyuterev fullname: Tyuterev, Vladimir email: vladimir.tyuterev@univ-reims.fr organization: Laboratory of Molecular Quantum Mechanics and Radiative Transfer, Tomsk State University – sequence: 2 givenname: Sergey surname: Tashkun fullname: Tashkun, Sergey organization: Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences – sequence: 3 givenname: Michael surname: Rey fullname: Rey, Michael organization: Groupe de Spectrométrie Moléculaire et Atmosphérique, Université de Reims – sequence: 4 givenname: Andrei orcidid: 0000-0002-4280-4096 surname: Nikitin fullname: Nikitin, Andrei organization: Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch, Russian Academy of Sciences |
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| CitedBy_id | crossref_primary_10_1016_j_chemphys_2024_112480 crossref_primary_10_1016_j_saa_2022_122071 crossref_primary_10_1016_j_saa_2023_122896 crossref_primary_10_1016_j_saa_2023_123456 crossref_primary_10_1002_qua_27378 crossref_primary_10_1016_j_jqsrt_2023_108616 crossref_primary_10_1063_5_0232298 crossref_primary_10_1016_j_jms_2023_111776 crossref_primary_10_1134_S1024856024700167 crossref_primary_10_3103_S002713142470024X crossref_primary_10_1016_j_jqsrt_2024_109196 crossref_primary_10_1134_S0036024424050121 crossref_primary_10_1016_j_jqsrt_2024_109098 crossref_primary_10_1016_j_jqsrt_2024_109286 |
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| SubjectTerms | Algorithms Computing time contact transformation Convergence Coupling (molecular) Couplings effective dipole transition moments Effective Hamiltonian Hamiltonian functions Mathematical models Molecular physics Molecular spectra Potential energy Resonant interactions Spectrum analysis symmetry Transformations (mathematics) Variational methods |
| Title | High-order contact transformations of molecular Hamiltonians: general approach, fast computational algorithm and convergence of ro-vibrational polyad models |
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