The effect of bending vibrations on the dipole moment of a linear polyatomic molecule: A theoretical treatment of the vibrational changes and transition moments |
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| Affiliation: | 1. School of Chemistry and Biochemistry Thapar University, Patiala 147 004, Punjab, India;2. Thapar University, Patiala 147004 Punjab, India;3. Department of Mechanical Engineering, Thapar University, Patiala, Punjab, India;1. Key Laboratory of Chemical Biology and Traditional Chinese Medicine Research and Key Laboratory of Resource Fine-Processing and Advanced Materials of Hunan Province of MOE, College of Chemistry and Chemical Engineering, Hunan Normal University, Changsha, Hunan 410081, China;2. Department of Chemistry, Lensfield Road, Cambridge University, UK;1. Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK;2. Synchrotron SOLEIL, L’Orme des Merisiers, Saint-Aubin, BP 48, 91192 Gif-sur-Yvette, France;3. Université de Lyon, Université Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, F-69622 Villeurbanne, France;4. Nano and Molecular Systems Research Unit, Faculty of Science, University of Oulu, P. O. Box 3000, 90014 Oulu, Finland;5. School of Chemistry, University of Nottingham, Nottingham NG7 2RD, UK;1. Department of Chemistry, Technical University of Denmark, DK-2800 Kongens Lyngby, Denmark;2. State Key Laboratory for Modification of Chemical Fibers and Polymer Materials, College of Materials Science and Engineering, Donghua University, Shanghai, PR China |
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| Abstract: | The vibrational effect on the dipole moment of a linear molecule is theoretically considered from the aspects of the dipole moment changes with the excitation of bending vibrations and the transition moments for the overtone, combination, and difference bands associated with bending modes. Such dipole moment changes and transition moments consist of two components, one depending on the first dipole moment derivatives with respect to bond lengths and the other depending on the second dipole moment derivatives with respect to bond angles. We show that the first component normally contributes little, and propose an approximation in which only the second component is retained. This approximation is practically important because the second component can be calculated without the anharmonic force constants. We derive formulas for the dipole moment changes and transition moments to facilitate a simultaneous analysis of different isotopic species. We introduce the concept of the equivalent mode, by which we may readily understand the correlation between the dipole moment change for a bending mode and the transition moment for a vibrational band. |
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