Tschöpe Martin, Feldmaier Matthias, Main Jörg, Hernandez Rigoberto
Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
Department of Chemistry, Johns Hopkins University, Baltimore, Maryland 21218, USA.
Phys Rev E. 2020 Feb;101(2-1):022219. doi: 10.1103/PhysRevE.101.022219.
Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition-state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on transition state theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.
多维系统中的化学反应通常由一个一阶鞍点来描述，其稳定流形和不稳定流形在正常双曲不变流形（NHIM）中相交。原则上，在NHIM上开始的轨迹在时间向前或向后传播时永远不会离开这个流形。然而，由于运动的不稳定性，对NHIM上的动力学进行数值研究很困难。我们应用神经网络来描述随时间变化的NHIM，并使用这个网络来稳定具有两个自由度的周期性驱动模型系统在NHIM上的运动。该方法使我们能够通过截面庞加莱曲面（PSOS）分析NHIM上的动力学，并将过渡态（TS）轨迹确定为与驱动鞍点具有相同周期性的周期轨道，即PSOS的一个被近可积环面包围的不动点。基于过渡态理论和周期性TS轨迹的弗洛凯分析，与传播大量轨迹系综相比，我们用显著减少的数值计算量计算了反应的速率常数。
