The exact isotope rule for symmetrically substituted molecules |
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| Institution: | 1. Department of Chemical & Biological Engineering, University of New Mexico, Albuquerque, NM, 87131, USA;2. Center for Micro-engineered Materials (CMEM), University of New Mexico, Albuquerque, NM, 87131, USA;1. Chemical Process Intensification, Chemical Engineering and Chemistry Department, Eindhoven University of Technology, Eindhoven, The Netherlands;2. Group of Energy Conversion Systems, Department of Energy, Politecnico di Milano, Milano, Italy;1. School of Energy and Chemical Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, Republic of Korea;2. Department of Energy Engineering, Ulsan National Institute of Science and Technology, 50 UNIST-gil, Eonyang-eup, Ulju-gun, Ulsan 44919, Republic of Korea;3. CarbonValue Co., Ltd., 2801 A-dong, 97, Centum Jungang-ro, Haeundae-gu, 48058 Busan, Republic of Korea |
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| Abstract: | The vibrational frequencies of isotopically substituted molecules are related exactly and explicitly to the parent molecules through a mixing parameter, following the method developed by Sheth (C. V. Sheth, J. Phys. B: Atom. molec. Phys. 8, 121 (1975)) using Cartesian displacement coordinates. It is shown that the explicit expressions for vibrational frequencies for symmetrical isotopic substitution of a non-linear X Y2-molecule coincide with that of DeWames and Wolfram (R. E. DeWames and T. Wolfram, J. chem. Phys. 40, 853 (1964)) derived from Green's function. The present procedure has the advantage of working with only symmetry coordinates belonging to genuine vibrations as compared to Green's function technique. Explicit expressions for vibrational frequencies for symmetrically substituted pyramidal X Y3-and tetrahedral X Y4-molecules are given for the first time involving properly defined mixing parameters. Using these expressions a theoretical justification of Noether's empirical rule (G. Herzberg, Infrared and Raman Spectra. Van Nostrand, New York (1945); H. D. Noether, J. chem. Phys. 11, 97 (1943)) is given for the first time in the cases considered. |
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