Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
J Chem Phys. 2019 Dec 28;151(24):244108. doi: 10.1063/1.5127539.
Chemical reactions in multidimensional driven systems are typically described by a time-dependent rank-1 saddle associated with one reaction and several orthogonal coordinates (including the solvent bath). To investigate reactions in such systems, we develop a fast and robust method-viz., local manifold analysis (LMA)-for computing the instantaneous decay rate of reactants. Specifically, it computes the instantaneous decay rates along saddle-bound trajectories near the activated complex by exploiting local properties of the stable and unstable manifold associated with the normally hyperbolic invariant manifold (NHIM). The LMA method offers substantial reduction in numerical effort and increased reliability in comparison with direct ensemble integration. It provides an instantaneous flux that can be assigned to every point on the NHIM and which is associated with a trajectory-regardless of whether it is periodic, quasiperiodic, or chaotic-that is bound on the NHIM. The time average of these fluxes in the driven system corresponds to the average rate through a given local section containing the corresponding point on the NHIM. We find good agreement between the results of the LMA and direct ensemble integration obtained using numerically constructed, recrossing-free dividing surfaces.
多维驱动系统中的化学反应通常由与一个反应和几个正交坐标（包括溶剂浴）相关的时变秩-1鞍点来描述。为了研究此类系统中的反应，我们开发了一种快速而稳健的方法——局部流形分析（LMA）——用于计算反应物的瞬时衰减率。具体来说，它通过利用与正规双曲线不变流形（NHIM）相关的稳定和不稳定流形的局部性质，在靠近激活复合物的鞍点轨迹上计算瞬时衰减率。与直接整体积分相比，LMA 方法在数值计算方面具有显著的减少工作量和提高可靠性的优势。它提供了一个瞬时通量，可以分配给 NHIM 上的每个点，并且与在 NHIM 上绑定的轨迹相关联，无论该轨迹是周期性的、准周期性的还是混沌的。在驱动系统中这些通量的时间平均值对应于通过包含 NHIM 上对应点的给定局部截面的平均速率。我们发现，使用数值构建的无重连分割面获得的 LMA 和直接整体积分的结果之间存在很好的一致性。
