Generalized Euler series transformation: application to the vibration-rotation energy level calculations of the H2,H3+, and H2O molecules

T. V. Kruglova; A. D. Bykov

doi:10.1117/12.724930

12 December 2006 Generalized Euler series transformation: application to the vibration-rotation energy level calculations of the H₂,H₃ ⁺, and H₂O molecules

T. V. Kruglova, A. D. Bykov

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Proceedings Volume 6580, 15th Symposium on High-Resolution Molecular Spectroscopy; 65800E (2006) https://doi.org/10.1117/12.724930
Event: 15th Symposium on High-Resolution Molecular Spectroscopy, 2006, Nizhny Novgorod, Russian Federation

Abstract

The Effective Hamiltonian method uses the perturbation expansions and the problem of series convergence are important. It was shown that poor convergence is typically observing for high-J levels and highly excited vibrational states. Several methods of resummation have been proposed, Pade and Borel methods, multivalued quadratic approximants, generating functions, Euler method. In this report the Euler series transformation is applied to summation of divergent series within the EH method. The calculations were performed for H₂, H₃ ⁺, H₂0 molecules.

Citation Download Citation

T. V. Kruglova and A. D. Bykov "Generalized Euler series transformation: application to the vibration-rotation energy level calculations of the H₂,H₃ ⁺, and H₂O molecules", Proc. SPIE 6580, 15th Symposium on High-Resolution Molecular Spectroscopy, 65800E (12 December 2006); https://doi.org/10.1117/12.724930

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