Wu Guozhen, Zhang Chenhui, Liu Zhaojun. Chaos in the Transitional States Induced by the Bending Motion[J]. Chinese Journal of Chemical Physics , 2004, 17(3): 263-268. doi: 10.1088/1674-0068/17/3/263-268
Citation: Wu Guozhen, Zhang Chenhui, Liu Zhaojun. Chaos in the Transitional States Induced by the Bending Motion[J]. Chinese Journal of Chemical Physics , 2004, 17(3): 263-268. doi: 10.1088/1674-0068/17/3/263-268

Chaos in the Transitional States Induced by the Bending Motion

doi: 10.1088/1674-0068/17/3/263-268
Funds:  Project supported by the National Natural Science Foundation of China(20373030).
  • Received Date: 2003-12-31
  • Molecular vibration is correlated to the motion of a pendulum and the lowly excited states are corresponding to that of the pendulum around its stable fixed point while the highly excited states are to the unstable fixed point. Specifically,the transitional state due to internal rotation is also corresponding to the unstable fixed point of the pendulum. As for a perturbed pendulum,chaos occurs first around its unstable fixed point,which is a reasonable consequence that the highly excited state and the transitional state are full with intrinsic chaotic motion. With this conjecture,HCN,its isomer HNC and the excited delocalized transitional state due to the internal rotation of H-C around the skeleton of C-N are interpreted with Morse oscillators in resonance. It is stressed that the delocalized transitional state is in multiple resonances between the H - C stretch and the bending due to that the classical bending frequency is lowered as the transitional state is approached. Multiple resonances,or the overlapping of resonances,lead to chaos as noted by Chirikov. Hence,the delocalzed transitional state can be in a chaotic state. Besides,the internal rotational state of HCP due to H atom is analyzed by this physical picture. For this purpose,an algebraic Hamiltonian for HCN,its isomer HNC and the delocalized transitional state is proposed with its coefficients elucidated by fitting with the quantal levels adopted from the literature by the quantum mechanical algorithm. The result shows that both the transitional state due to the internal rotation of H atom and the highly excited states of HCN and HNC are full of multiple resonances. Therefore,chaos is expected for these systems. Finally,all these ideas are compounded by a proposed model for unfolding the characteristics of chaos in the molecular system.
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Chaos in the Transitional States Induced by the Bending Motion

doi: 10.1088/1674-0068/17/3/263-268
Funds:  Project supported by the National Natural Science Foundation of China(20373030).

Abstract: Molecular vibration is correlated to the motion of a pendulum and the lowly excited states are corresponding to that of the pendulum around its stable fixed point while the highly excited states are to the unstable fixed point. Specifically,the transitional state due to internal rotation is also corresponding to the unstable fixed point of the pendulum. As for a perturbed pendulum,chaos occurs first around its unstable fixed point,which is a reasonable consequence that the highly excited state and the transitional state are full with intrinsic chaotic motion. With this conjecture,HCN,its isomer HNC and the excited delocalized transitional state due to the internal rotation of H-C around the skeleton of C-N are interpreted with Morse oscillators in resonance. It is stressed that the delocalized transitional state is in multiple resonances between the H - C stretch and the bending due to that the classical bending frequency is lowered as the transitional state is approached. Multiple resonances,or the overlapping of resonances,lead to chaos as noted by Chirikov. Hence,the delocalzed transitional state can be in a chaotic state. Besides,the internal rotational state of HCP due to H atom is analyzed by this physical picture. For this purpose,an algebraic Hamiltonian for HCN,its isomer HNC and the delocalized transitional state is proposed with its coefficients elucidated by fitting with the quantal levels adopted from the literature by the quantum mechanical algorithm. The result shows that both the transitional state due to the internal rotation of H atom and the highly excited states of HCN and HNC are full of multiple resonances. Therefore,chaos is expected for these systems. Finally,all these ideas are compounded by a proposed model for unfolding the characteristics of chaos in the molecular system.

Wu Guozhen, Zhang Chenhui, Liu Zhaojun. Chaos in the Transitional States Induced by the Bending Motion[J]. Chinese Journal of Chemical Physics , 2004, 17(3): 263-268. doi: 10.1088/1674-0068/17/3/263-268
Citation: Wu Guozhen, Zhang Chenhui, Liu Zhaojun. Chaos in the Transitional States Induced by the Bending Motion[J]. Chinese Journal of Chemical Physics , 2004, 17(3): 263-268. doi: 10.1088/1674-0068/17/3/263-268

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