Application of the contact transformation method to torsional problems in methyl silane |
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| Institution: | 1. School of Finance, Anhui University of Finance & Economics, Bengbu 233030, China;2. School of Management and Engineering, Nanjing University, Nanjing 210093, China;1. Department of Geology and Geophysics, University of Oklahoma, Norman, OK 73019, USA;2. MRC Laboratory of Molecular Biology, Francis Crick Avenue, Cambridge CB2 0QH, UK;3. Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA;1. Key Laboratory of Ministry of Education for Electronic Equipment Structure Design, Xidian University, Xi''an, 710071, PR China;2. Department of Electrical and Computer Engineering, Tandon School of Engineering, New York University, NY 11201, USA;3. State Key Laboratory for Manufacturing Systems Engineering, Xi''an Jiaotong University, Xi''an 710049, PR China;4. School of Rail Transportation, Soochow University, Suzhou, Jiangsu 215137, PR China;1. School of Electrical Engineering, Korea University, 145 Anam-ro, Seongbuk-gu, Seoul 02841, Republic of Korea;2. Medical Information Research Section, Electronics and Telecommunications Research Institute, 218 Gajeong-ro, Yuseong-gu, Daejeon 34129, Republic of Korea;1. Department of Physics, Khalifa University, P. O. Box 127788, Abu Dhabi, United Arab Emirates;2. Department of Applied Mathematics and Sciences, Khalifa University, P. O. Box 127788, Abu Dhabi, United Arab Emirates;3. Center for Cyber-Physical Systems (C2PS), Khalifa University, P. O. Box 127788, Abu Dhabi, United Arab Emirates |
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| Abstract: | The effect of the torsional degree of freedom on redundancies in the Hamiltonian and on the dipole operator has been investigated for methyl silane-like molecules. By applying a rotational contact transformation to the torsion-rotation Hamiltonian HTR for the ground vibrational state, a systematic method is demonstrated for treating the redundancies that relate different terms in HTR. In general, with this method, the experimentally accessible molecular parameters in the reduced Hamiltonian can be related to the physically significant molecular parameters in the untransformed Hamiltonian. It is shown that HTR contains a new term which has matrix elements with selection rules (ΔK = ±3), (Δσ = 0), and ΔvT arbitrary, where vT and σ label the torsional levels and sublevels, respectively. As a result of this term, the distortion dipole constant μD which characterizes (ΔK = ±3) matrix elements in C3v molecules cannot, in systems like CH3SiH3, be ascribed entirely to centrifugal distortion but can contain a significant contribution from torsional effects. Furthermore, new transitions can appear in the pure torsional bands which may be strong enough to observe in low barrier molecules. By applying a vibrational contact transformation, the form is derived of the leading torsional terms in the dipole moment expansion. The four dipole distortion constants μ0T, μ2T, μ|;T, and μΛT which characterize these terms are related to the molecular parameters that enter the Coriolis, centrifugal distortion, and anharmonicity contributions to the vibration-torsion-rotation Hamiltonian. |
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