Vanden-Eijnden Eric, Tal Fabio A
Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA.
J Chem Phys. 2005 Nov 8;123(18):184103. doi: 10.1063/1.2102898.
Transition state theory (TST) is revisited, as well as evolutions upon TST such as variational TST in which the TST dividing surface is optimized so as to minimize the rate of recrossing through this surface and methods which aim at computing dynamical corrections to the TST transition rate constant. The theory is discussed from an original viewpoint. It is shown how to compute exactly the mean frequency of transition between two predefined sets which either partition phase space (as in TST) or are taken to be well-separated metastable sets corresponding to long-lived conformation states (as necessary to obtain the actual transition rate constants between these states). Exact and approximate criterions for the optimal TST dividing surface with minimum recrossing rate are derived. Some issues about the definition and meaning of the free energy in the context of TST are also discussed. Finally precise error estimates for the numerical procedure to evaluate the transmission coefficient kappaS of the TST dividing surface are given, and it is shown that the relative error on kappaS scales as 1/square root(kappaS) when kappaS is small. This implies that dynamical corrections to the TST rate constant can be computed efficiently if and only if the TST dividing surface has a transmission coefficient kappaS which is not too small. In particular, the TST dividing surface must be optimized upon (for otherwise kappaS is generally very small), but this may not be sufficient to make the procedure numerically efficient (because the optimal dividing surface has maximum kappaS, but this coefficient may still be very small).
本文重新审视了过渡态理论（TST），以及基于TST的发展，如变分TST，其中TST的分割面经过优化，以最小化穿过该表面的再穿越率，还有旨在计算对TST跃迁速率常数的动力学修正的方法。从一个全新的视角对该理论进行了讨论。展示了如何精确计算两个预定义集合之间跃迁的平均频率，这两个集合要么划分相空间（如在TST中），要么被视为对应于长寿命构象状态的分离良好的亚稳态集合（这对于获得这些状态之间的实际跃迁速率常数是必要的）。推导了具有最小再穿越率的最优TST分割面的精确和近似标准。还讨论了在TST背景下自由能的定义和意义的一些问题。最后给出了评估TST分割面传输系数κS的数值程序的精确误差估计，并表明当κS较小时，κS的相对误差与1/√κS成比例。这意味着，只有当TST分割面的传输系数κS不太小时，才能有效地计算对TST速率常数的动力学修正。特别是，必须对TST分割面进行优化（否则κS通常非常小），但这可能不足以使该程序在数值上有效（因为最优分割面具有最大的κS，但该系数可能仍然非常小）。
