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
Hauptverfasser: Tyuterev, Vladimir, Tashkun, Sergey, Rey, Michael, Nikitin, Andrei
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Abingdon Taylor & Francis 18.08.2022
Taylor & Francis Ltd
Schlagworte:
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
ISSN:0026-8976, 1362-3028
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Zusammenfassung: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.
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ISSN:0026-8976
1362-3028
DOI:10.1080/00268976.2022.2096140