Pavlov-Verevkin V B, Lorquet J C
Department of Chemistry, University of Liège, Sart-Tilman, Building B6, B-4000 Liège 1, Belgium.
J Chem Phys. 2005 Aug 15;123(7):074324. doi: 10.1063/1.2006107.
Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an angle-action reaction path Hamiltonian (RPH). The accuracy of the vibrational adiabatic approximation is found to be completely independent of the shape of the potential energy Vs. Vibrations are adiabatic when two independent dimensionless parameters are small. The first one, denoted as sigma, controls the dynamic coupling. The physical significance of the condition sigma<<1 is that the amplitude of the vibrations normal to the reaction path should be much smaller than the radius of curvature of the reaction path. The second parameter, denoted as mu, governs the static coupling. It results from the dependence of the vibrational frequency omega on the reaction coordinate s. The higher omega, the lower its derivative with respect to s and, more unexpectedly, the higher the translational energy epsilon, the lower mu is. A criterion for locating a particular dividing surface in barrierless reactions is proposed. This surface separates two regions of space: one where energy flows freely, and one where energy conversion between translation and vibration is hindered by adiabatic invariance. The nature of the dynamical constraint that prevents the product translational energy distribution from being fully statistical can be identified by a maximum entropy analysis. The constraint is found to bear on the translational momentum ps, i.e., on the square root of the translational energy epsilon1/2. This can be understood by applying Jacobi's form of the least action principle to the vibrationally adiabatic RPH.
单分子反应最后一步中平动能向振动能的转化是由反应路径的曲率引起的。通过角 - 作用反应路径哈密顿量（RPH）分析相应的耦合。发现振动绝热近似的精度与势能(V_s)的形状完全无关。当两个独立的无量纲参数很小时，振动是绝热的。第一个参数记为(\sigma)，控制动态耦合。(\sigma\ll1)这一条件的物理意义是垂直于反应路径的振动幅度应远小于反应路径的曲率半径。第二个参数记为(\mu)，控制静态耦合。它源于振动频率(\omega)对反应坐标(s)的依赖。(\omega)越高，其对(s)的导数越低，更出乎意料的是，平动能(\epsilon)越高，(\mu)越低。提出了在无势垒反应中定位特定分界面的判据。这个面将空间的两个区域分开：一个区域能量自由流动，另一个区域平动和振动之间的能量转换因绝热不变性而受阻。通过最大熵分析可以确定阻止产物平动能分布完全统计的动力学约束的性质。发现该约束作用于平动动量(p_s)，即平动能(\epsilon^{1/2})的平方根。这可以通过将雅可比形式的最小作用原理应用于振动绝热RPH来理解。
