Reaction Path Topology at Conical Intersections

分子是由被电子束缚在一起的原子核组成的。将原子核结合在一起的能量随着它们的相对位置而变化，看起来像一个景观，这被称为势能面。化学反应通常可以通过将原子核可视化为在势能面上滚动的微小滚珠来描述。原子核所遵循的路径被称为反应路径：它将景观上的稳定起点和终点连接在一起，这些起点和终点对应于试剂和产物分子。然而，有时候，这个简单的图像会被打破，因为可能存在两个势能面，一个比另一个能量高，它们在原子核的特定几何形状下聚集在一起，形成一个漏斗形的物体，称为“圆锥形交叉”。通常，圆锥形交叉发生在光激活反应中，例如在光合作用和视觉中发现的。通过吸收光能，分子跳跃到上表面;当它们随后反应时，它们可以通过沿着锥形交叉漏斗向下传递的反应路径快速松弛到下表面。这个过程相当于电子和原子核之间的能量交换，是高度量子力学的。因此，原子核的运动不再被视为滚珠轴承在势面上滚动。相反，它必须被可视化为一个波函数，它在两个潜在的表面上延伸，并描述了一个复杂的耦合运动在附近的锥形交叉漏斗。这项研究的目的是更多地了解这种波函数内部发生的事情。在最近的工作中，申请人发现，当波函数被限制在两个势面中较低的一个（从而包围漏斗的底部）时，它满足拓扑定理，该定理允许它被分成两部分：一部分包含所有沿顺时针方向围绕漏斗的反应路径，另一部分包含反轨道路径。这一定理的最新应用解决了氢交换反应实验数据中的一个长期难题，这导致了一个通用理论，解释了“Berry相”（一种通过在圆锥形交叉点周围循环产生的效应）对化学反应机制和速率的影响[Science 309，1227（2005）]。我们建议扩展这一理论，以处理反应不限于底部的漏斗，但可以通过它，从表面到表面。新理论将把这些反应的波函数分解成所有拓扑上不同的反应路径;每条路径将是环（围绕漏斗）和跳（在两个表面之间）的组合。该理论将显示这些类型的反应路径之间的相互作用如何促进或阻碍通过漏斗，这将导致一个一般的理论解释拓扑结构对反应机制和锥形交叉点的速率的影响。为了发展这一理论，我们将把它结合到氢交换反应的精确量子模拟中，这将允许与Zare小组（斯坦福大学）测量的新实验数据进行直接比较。这将允许拓扑结构被精炼或消除，从而引导我们走向理论的最终形式。在发展理论之后，我们将使用它来提高各种近似方法的效率和解释能力，这些方法可用于模拟溶液中发生的复杂的捕光反应。

Molecules consist of atomic nuclei bound together by electrons. The energy that binds the nuclei together varies as a function of their relative position, and looks like a landscape, which is called a potential energy surface. A chemical reaction can usually be described by visualising atomic nuclei as tiny ball bearings rolling over the potential energy landscape. The path that the nuclei follow is called a reaction path: it connects together stable starting and end points on the landscape, which correspond to the reagent and product molecules. Sometimes, however, this simple picture breaks down, because there can exist two potential energy surfaces, one higher in energy than the other, which come together at a particular geometry of the nuclei, to form a funnel-shaped object called a 'conical intersection'. Typically, conical intersections occur in light-activated reactions, such as are found in photosynthesis and vision. By absorbing the light-energy, the molecules jump onto the upper surface; when they subsequently react, they may relax rapidly to the lower surface by following a reaction path which passes down the conical intersection funnel. This process is equivalent to exchanging energy between the electrons and the atomic nuclei, and is highly quantum mechanical. As a result, the motion of the nuclei can no longer be visualised as ball bearings rolling on a potential surface. Instead it must be visualised as a wave function, which extends over both the potential surfaces, and describes a complicated coupled motion in the vicinity of the conical intersection funnel. The aim of the proposed research is to understand more about what goes on inside such a wave function. In recent work, the applicant found that, when the wave function is confined to the lower of the two potential surfaces (and thus encircles the base of the funnel), it satisfies a topological theorem which allows it to be split into two pieces: one piece contains all the reaction paths that loop in a clockwise direction around the funnel, the other piece contains the anticlockwise paths. The recent application of this theorem solved a longstanding puzzle in experimental data measured for the hydrogen-exchange reaction, and this led to a general theory explaining the effect of the 'Berry phase' (an effect produced by looping around conical intersections) on chemical reaction mechanisms and rates [Science 309, 1227 (2005)]. We propose extending this theory to treat reactions which are not confined to the base of the funnel, but which can pass through it, from surface-to-surface. The new theory will decompose the wave functions of such reactions into all topologically distinct reaction paths; each path will be a combination of loops (around the funnel) and hops (between the two surfaces). The theory will show how the interaction between these types of reaction path facilitates or impedes passage through the funnel, and this will result in a general theory explaining the effect of topology on reaction mechanisms and rates at conical intersections. To develop the theory, we will incorporate it into accurate quantum simulations on the hydrogen-exchange reaction, which will permit direct comparison with new experimental data to be measured by the Zare group (Stanford). This will permit topological conjectures to be refined or eliminated, thus guiding us towards the final form of the theory. After developing the theory, we will use it to improve the efficiency and interpretational power of a variety of approximate methods which can be used to simulate complex light-harvesting reactions that take place in solution.