1999
DOI: 10.1006/jmsp.1999.7811
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Algebraic Description of Anharmonic Stretching Vibrations

Abstract: A U(2) algebraic model is presented to describe stretching vibrations of XYn (n = 2, 3, and 4) systems, where anharmonic interactions between the bond modes are considered. This model in a limit corresponds to an anharmonically coupled local-mode model. As an example, the model for a molecule XY4 is applied to recently observed spectra of methane in both gas and liquid phases, and the results obtained are in good agreement with the experiments. Copyright 1999 Academic Press.

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Cited by 9 publications
(3 citation statements)
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“…Others developments based upon this SU (2) formalism have been proposed by Lemus and Franck [13] and by Xi-Wen Hou et al [14]. Alternatively, an algebraic formalism based on unitary groups, initially developed by Michelot et al [15] and Leroy et al [16][17][18][19], has shown to be well efficient to reproduce the vibrational levels of XY 4 molecular systems.…”
Section: Introductionmentioning
confidence: 97%
“…Others developments based upon this SU (2) formalism have been proposed by Lemus and Franck [13] and by Xi-Wen Hou et al [14]. Alternatively, an algebraic formalism based on unitary groups, initially developed by Michelot et al [15] and Leroy et al [16][17][18][19], has shown to be well efficient to reproduce the vibrational levels of XY 4 molecular systems.…”
Section: Introductionmentioning
confidence: 97%
“…However, this model becomes rather complex when the number of atoms is more than 4. Based on the properties of the unitary and special unitary groups, many teams have developed quite different models applied to the vibrational modes of molecular systems and it is worth to mention the works of Van Roosmalen et al [3,4], Lemus and Franck [5] or Hou et al [6]. Interpreting differently the properties of the unitary groups, an algebraic formalism called the U(p + 1) formalism, initially developed by Michelot and Moret-Bailly [7] and Leroy et al [8][9][10][11], has demonstrated its efficiency to reproduce the vibrational level of XY 4 molecular systems, and recently for XY 3 molecular systems such as the stretching modes of AsH 3 [12] and the vibrational modes of the stibine molecule [13].…”
Section: Introductionmentioning
confidence: 99%
“…[1−6] A simple algebraic method is based on algebra U (2), which provides good fits to stretching vibrational spectra of polyatomic molecules. [3] Recently, an important development on algebraic approaches is to incorporate bending vibrations of polyatomic molecules. Sample molecules such as X 3 , [4] XY 2 , [5] and XY 4 [6] have been studied via algebraic methods.…”
Section: Introductionmentioning
confidence: 99%