Symmetrization and elimination of redundancies in the vibrational eigenvalue problem |
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| Affiliation: | 1. Department of Analytical Chemistry, Faculty of Chemistry, Razi University, Kermanshah 671496734, Iran;2. Laboratorio de Desarrollo Analítico y Quimiometría (LADAQ), Cátedra de Química Analítica I, Universidad Nacional del Litoral, Ciudad Universitaria, CC 242 (S3000ZAA), Santa Fe, Argentina;1. V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, 1, Akademichesky Avenue, 634055 Tomsk, Russian Federation;2. Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, Université de Reims, U.F.R. Sciences, B.P. 1039, 51687 Reims Cedex 2, France;3. AILES Beamline, Synchrotron SOLEIL, L''Orme des Merisiers, St-Aubin BP48, F-91192 Gif-sur-Yvette Cedex, France.;4. Sorbonne Université, CNRS, MONARIS, UMR 8233, 4 place Jussieu, Paris, France;5. Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109, USA;6. QUAMER,Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russian Federation;1. Laboratory of Theoretical Spectroscopy, V.E. Zuev Institute of Atmospheric Optics, Russian Academy of Sciences, 1, Akademichesky Avenue, 634055 Tomsk, Russian Federation;2. QUAMER, Tomsk State University, 36 Lenin Avenue, 634050 Tomsk, Russian Federation;3. Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, Université de Reims, U.F.R. Sciences, B.P. 1039, 51687 Reims Cedex 2, France;4. Univ. Grenoble Alpes, LIPhy, F-38000 Grenoble, France;5. CNRS, LIPhy, F-38000 Grenoble, France |
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| Abstract: | A method convenient for computer programming of the solution of the eigenvalue equation GFL = LΛ is presented. Its essential feature is a transformation by a triangular matrix V which simultaneously symmetrizes the product GF (VV2 = G) and eliminates the redundancies. Also a left inverse of V is derived, which is of importance for the calculation of vibration rotation interaction constants. An algorithm for the computation of these matrices is available from the editor or the author. |
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