# QUALITATIVE APPROACH TO MOLECULAR DYNAMICS: NONLINEAR NORMAL MODES AND LOCALIZED VIBRATIONS

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 Title: QUALITATIVE APPROACH TO MOLECULAR DYNAMICS: NONLINEAR NORMAL MODES AND LOCALIZED VIBRATIONS Creators: Sadovskii, D.; Zhilinskii, B. Issue Date: 1992 Publisher: Ohio State University Abstract: The concept of a simplest Hamiltonian based on the topological properties of a reduced phase space stratified under the action of the symmetry group of the problem leads to the introduction of non-linear normal modes, the same as first suggested by Montaldi, Stewart, and Roberts, Phil. Trans. R. Soc. Lond. A325, 237(1988). The approach is illustrated on the example of a double degenerate $D_{3}$-symmetric oscillator, such as the H\’{e}non-Heiles problem, or the bending vibration of an $X_{3}$ molecule. In the latter case stationary of the simplest Hamiltonian are associated with the periodic trajectories in the initial phase space, and have a clear configuration image. Generalization to the n-mode case with the ST(n) dynamical symmetry is discussed. [FIGURE] Description: Author Institution: Herzberg Institute of Astrophysics, National Research Council of Canada; Department of Chemistry Laboratoire de Spectronomie Mol\'{e}culaire et Instrumentation Laser (SMIL), Moscow State University Universit\'{e} de Bourgogne URI: http://hdl.handle.net/1811/12731 Other Identifiers: 1992-RA-05