Kramers-Fokker-Planck equation for polyatomic molecules
Kramers-Fokker-Planck equation for polyatomic molecules
复制标题
多原子分子的 Kramers-Fokker-Planck 方程
DOI：
10.1063/1.1502250
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发表时间：
2002
影响因子：
4.4
通讯作者：
Y. Maruyama
中科院分区：
文献类型：
--
作者：
M. Nagaoka;T. Okamoto;Y. Maruyama
从整个溶液系统的微观哈密顿量出发，利用Zubarev的非平衡统计分布函数技术，导出了多原子分子的KFP方程。为此，在自由能面上的一个固定点定义了溶质分子的一组法向坐标。在正坐标表示中，KFP方程的表达式不仅包括科里奥利耦合引起的变形，还包括引起新型耦合的摩擦张量。为了证明这一点，我们检查了两个例子。首先，在快速变量绝热消去近似下，由上述KFP方程推导出一维KFP方程，该方程对应于Kramers首次直观推导出的一维溶液化学反应模型方程。其次，假设一个模型系统同时描述了一对振动和旋转运动，一个二维…
Starting from the microscopic Hamiltonian of a whole solution system, we have derived a Kramers–Fokker–Planck (KFP) equation for polyatomic molecules by using Zubarev’s techinique of nonequilibrium statistical distribution function. For the purpose, a set of normal coordinates of a solute molecule is defined at a stationary point on the free energy surface. In the normal coordinate representation, the expression of the KFP equation includes not only the deformation originating in the Coriolis coupling but also the friction tensor inducing a new type of coupling. For demonstration, two examples are examined. First, under the approximation of adiabatic elimination of fast variables, a one-dimensional KFP equation is derived from the above KFP equation, which corresponds to the equation that Kramers first derived intuitively for one-dimensional chemical reaction model in solution. Second, assuming a model system which describes simultaneously a couple of vibrational and rotational motions, a two-dimensional ...