分子高激发振动的经典代数方法研究——以C_2H_2的C-H弯曲振动为例

本文以目前探讨得较多的C2H2的CH弯曲振动为例,说明如何应用代数方法来研究分子的高激发振动。由于分子的高激发振动态具有很强的模间非线性偶合以及能量的传递,传统的动力学方法似乎很难有效地用来研究其性质。问题的核心是高激发振动态由于其量子数很大,因此具有经典(或半经典)的性质。同时模间能量的传递可以用二次量子化算子来表示,而这些算子所具有的代数性质,使得人们可以用几何的概念来描述其性质。因此,整个问题就变为用几何的观点来分析分子的高激发振动态。最后,我们用所得的经典的代数哈密顿量和哈密顿方程对CHtrans弯曲和cis弯曲振动模间能量的传递速度与体系所含能量之高低的关系做了探讨

The classical Algebraic Study on the Molecular Highly Excited Vibration-a Case Study of the C-H Bend Motion of C_2H_2

An algebraic method is proposed for the study of the highly excited bend motion of C 2H 2. The approach is based on a classical picture taking into account the nonlinear and inter mode couplings. The system is considered as classical based on the fact that the highly excited vibration is of high energy and approaches the classical realm. The inter mode couplings can be represented by the second quantization operators which, in turn, can be cast into a geomtric picture due to their algebraic properties. Hence, the whole dynamical picture is a geometric one. This enables us to study the dynamics from a geometric point of view. Finally, the obtained calssical algebraic Hamiltonian together with Hamilton's equations of motion is employed to study the energy transfer rate between the trans and cis bends as a function of the system energy.