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首页> 外文期刊>The journal of physical chemistry, C. Nanomaterials and interfaces >Equilibrium and Recrossings of the Transition State: What Can Be Learned from Diffusion?
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Equilibrium and Recrossings of the Transition State: What Can Be Learned from Diffusion?

机译：过渡态的平衡与交叉：从扩散中学到什么？

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We examine the assumptions and conclusion of (generalized) transition state theory (GTST) by considering the activation process in the diffusion (Langevin) limit. We find the asymptotic structure of the leading eigenfunctions and eigenvalues of the Fokker-Planck operator with a bistable potential and hence the longtime quasi-equilibrium behavior of the phase space probability density function (pdf). Defining reactant and product as small neighborhoods of the stable states, we examine all possible recrossings of the transition state region (TSR) and find their contribution to the mean first passage time (MFPT) from one state to the other. We show that the mean number of recrossings of the TSR is 1, so the MFPT from one state to the other is twice that to the stochastic separatrix, which we use as a generalized transition state (GTS). The activation rate, that is, the rate at which trajectories arrive from one state to the other, is then shown to be one-half of the arrival rate at the GTS and in the limit of a high barrier is independent of the choice of the size of the domains that define the states. We conclude that to obtain the correct rate in (G)TST (i) the quasi-equilibrium density (qepdf) rather than the equilibrium density (epdf) has to be used, (ii) the qepdf contains a boundary layer near the stochastic separatrix, but otherwise the reactant qepdf is nearly equal the epdf, and (iii) all recrossings of the (G)TS are accounted for if the (G)TS is the stochastic separatrix, but not otherwise. We also consider the case of a single metastable state.
机译：我们通过考虑扩散（兰开芬）极限中的活化过程来研究（广义）过渡态理论（GTST）的假设和结论。我们发现具有双稳态势的Fokker-Planck算子的先导特征函数和特征值的渐近结构，从而发现了相空间概率密度函数（pdf）的长期拟平衡行为。将反应物和产物定义为稳定态的小邻域，我们研究了过渡态区域（TSR）的所有可能的重交，并发现它们对从一种状态到另一种状态的平均首次通过时间（MFPT）的贡献。我们表明，TSR的平均交叉次数为1，因此从一个状态到另一状态的MFPT是到随机分离的MFPT的两倍，我们将其用作广义过渡状态（GTS）。激活速率，即轨迹从一种状态到达另一种状态的速率，则显示为GTS到达速率的一半，并且在高障碍的范围内，与激活状态的选择无关。定义状态的域的大小。我们得出结论，为了在（G）TST中获得正确的速率，（i）必须使用准平衡密度（qepdf）而不是平衡密度（epdf），（ii）qepdf在随机分离层附近包含边界层，但否则，反应物qepdf几乎等于epdf，并且（iii）如果（G）TS是随机的分离层，则说明（G）TS的所有重交，但不是这样。我们还考虑了单个亚稳态的情况。

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