Abstract
A Fermi resonance-algebraic model is proposed for molecular vibrations, where aU(2) algebra is used for describing the vibrations of each bond, and Fermi resonances between stretching and bending modes are taken into account. The model for a bent moleculeXY 2 and a moleculeXY 3 is successfully applied to fitting the recently obsenred vibrational spectrum of the water molecule and arsine (AsH3), respectively, and the results are compared with those of other models. Calculations show that algebraic approaches can be used as an effective method to describe molecular vibrations with small standard deviations.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Oss, S., Algebraic models in molecular spectroscopy,Adv. Chem. Phys., 1996, 93: 455.
Frank, A., Lemus, R., Bijker, R. et al., A general algebraic model for molecular vibrational spectroscopy,Ann. Phys. (N.Y.), 1996, 252: 211.
Cooper, I. L., Gupta, R. K., Application ofU (2) 3O (2) andU (2) 3U(1) dynamical symmetries to diatomic molecular vibrations,Phys. Rev. A, 1997, 55(6): 4112.
Ping, J. L., Chen, J. Q., Partial dynamical symmetry in molecules,Ann. Phys. (N. Y.), 1997, 255: 75.
HOU, X. W., Dong, S. H., Xie, M. et al., Algebraic approach to vibrational spectra of tetrahedral molecules: A case study of silicon tetrafluoride,Chem. Phys. Lett., 1998, 283: 173.
Iachello, F., Oss, S., Algebraic approach to molecular spectra: two-dimensional problems,J. Chem. Phys., 1996, 104 (18): 6956.
Ma, Z. Q., Hou, X. W., Xie, M., Boson-realization model for the vibrational spectra of tetrahedral molecules,Phys. Rev. A, 1996, 53(4): 2173.
Halonen, L., Carrington, T., Jr., Fermi resonances and local modes in water, hydrogen sulfide, and hydrogen selenide,J. Chem. Phys., 1988, 88(7): 4171.
Lukka, T., Kauppi, E., Halonen, L., Fermi resonances and local modes in pyramidal XH3 molecules: an application to arsine (AsH3) overtone spectra,J. Chem. Phys., 1995, 102(13): 5200.
Hou, X. W., Xie, M., Ma, Z. Q., Boson-realization model applied to highly excited vibrations of H2O,Phys. Rev. A, 1997, 55(5): 3401.
HOU, X. W., Xie, M., Dong, S. H. et al., Overtone spectra and intensities of tetrahedral molecules in boson-realization models,Ann. Phys. (N.Y.), 1998, 263: 340.
Law, M. M., Duncan, J. L., Local mode and normal mode stretching vibrations inXH 4 andXH 3 systems: beyond thex, K relations,Mol. Phys., 1994, 83(4): 757.
Chen, X., Gou, Q., Pang, X., Calculation of vibrational energy spectra of H20 molecule by nonlinear quantum theory,Chin. Phys. Lett., 1996, 13(9): 660.
Xie, D., Yan, G., The potential energy surface and the highly excited vibrational band origins of the water molecule,Chem. Phys. Lett., 1996. 248: 409.
Ulenikov, 0. N., Sun, F., Wang, X. et al., High resolution spectroscopic study of arsine: 3vl and 2v1 + v3, dyad: the tendency of symmetry reduction,J. Chem. Phys., 1996, 105(17): 7310.
Author information
Authors and Affiliations
Additional information
Project supported by the National Natural Science Foundation of China (Grant No. 19377103) and the Chinese Academy of Sciences.
Rights and permissions
About this article
Cite this article
Hou, X., Dong, S., Xie, M. et al. Fermi resonance-algebraic model for molecular vibrational spectra. Sci. China Ser. A-Math. 42, 207–212 (1999). https://doi.org/10.1007/BF02876573
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02876573