Bond breaking in a Morse chain under tension: fragmentation patterns, higher index saddles, and bond healing.

We investigate the fragmentation dynamics of an atomic chain under tensile stress. We have classified the location, stability type (indices), and energy of all equilibria for the general n-particle chain, and have highlighted the importance of saddle points with index >1. We show that for an n = 2-particle chain under tensile stress the index 2 saddle plays a central role in organizing the dynamics. We apply normal form theory to analyze phase space structure and dynamics in a neighborhood of the index 2 saddle. We define a phase dividing surface (DS) that enables us to classify trajectories passing through a neighborhood of the saddle point using the values of the integrals associated with the normal form. We also generalize our definition of the dividing surface and define an extended dividing surface (EDS), which is used to sample and classify all trajectories that pass through a phase space neighborhood of the index 2 saddle at total energies less than that of the saddle. Classical trajectory simulations are used to study fragmentation patterns for the n = 2 chain under tension. That is, we investigate the relative probability for breaking one bond versus concerted fission of several (two, in this case) bonds. Initial conditions for trajectories are obtained by sampling the EDS at constant energy. We sample trajectories at fixed energies both above and below the energy of the saddle. The fate of trajectories (single versus multiple bond breakage) is explored as a function of the location of the initial condition on the EDS, and a connection made to the work of Chesnavich on collision-induced dissociation. A significant finding is that we can readily identify trajectories that exhibit bond healing. Such trajectories pass outside the nominal (index 1) transition state for single bond dissociation, but return to the potential well region, possibly several times, before ultimately dissociating.

我们研究了在拉伸应力下原子链的断裂动力学。我们对一般的\(n\)粒子链的所有平衡点的位置、稳定性类型（指标）和能量进行了分类，并强调了指标\(>1\)的鞍点的重要性。我们表明，对于在拉伸应力下的\(n = 2\)粒子链，指标\(2\)的鞍点在组织动力学方面起着核心作用。我们应用范式理论来分析指标\(2\)鞍点附近的相空间结构和动力学。我们定义了一个相分界面（\(DS\)），它使我们能够利用与范式相关的积分值对通过鞍点附近的轨迹进行分类。我们还推广了分界面的定义，并定义了一个扩展分界面（\(EDS\)），它用于对在总能量小于鞍点能量的情况下通过指标\(2\)鞍点的相空间邻域的所有轨迹进行采样和分类。经典轨迹模拟被用于研究在张力下\(n = 2\)链的断裂模式。也就是说，我们研究了断裂一个键与几个（在这种情况下是两个）键协同裂变的相对概率。轨迹的初始条件是通过在恒定能量下对\(EDS\)进行采样获得的。我们在鞍点能量之上和之下的固定能量处对轨迹进行采样。轨迹的归宿（单键断裂与多键断裂）作为初始条件在\(EDS\)上的位置的函数进行了探究，并与切斯纳维奇关于碰撞诱导解离的工作建立了联系。一个重要的发现是，我们可以很容易地识别出表现出键愈合的轨迹。这样的轨迹在单键解离的标称（指标\(1\)）过渡态之外通过，但在最终解离之前可能会多次返回势阱区域。