Department of Basic Science, The University of Tokyo, Komaba, 153-8902 Tokyo, Japan.
J Chem Phys. 2012 Dec 14;137(22):22A520. doi: 10.1063/1.4742155.
We develop a theory and the method of its application for chemical dynamics in systems, in which the adiabatic potential energy hyper-surfaces (PES) are densely quasi-degenerate to each other in a wide range of molecular geometry. Such adiabatic electronic states tend to couple each other through strong nonadiabatic interactions. Technically, therefore, it is often extremely hard to accurately single out the individual PES in those systems. Moreover, due to the mutual nonadiabatic couplings that may spread wide in space and due to the energy-time uncertainty relation, the notion of the isolated and well-defined potential energy surface should lose the sense. On the other hand, such dense electronic states should offer a very interesting molecular field in which chemical reactions to proceed in characteristic manners. However, to treat these systems, the standard theoretical framework of chemical reaction dynamics, which starts from the Born-Oppenheimer approximation and ends up with quantum nuclear wavepacket dynamics, is not very useful. We here explore this problem with our developed nonadiabatic electron wavepacket theory, which we call the phase-space averaging and natural branching (PSANB) method [T. Yonehara and K. Takatsuka, J. Chem. Phys. 129, 134109 (2008)], or branching-path representation, in which the packets are propagated in time along the non-Born-Oppenheimer branching paths. In this paper, after outlining the basic theory, we examine using a one-dimensional model how well the PSANB method works with such densely quasi-degenerate nonadiabatic systems. To do so, we compare the performance of PSANB with the full quantum mechanical results and those given by the fewest switches surface hopping (FSSH) method, which is known to be one of the most reliable and flexible methods to date. It turns out that the PSANB electron wavepacket approach actually yields very good results with far fewer initial sampling paths. Then we apply the electron wavepacket dynamics in path-branching representation and the so-called semiclassical Ehrenfest theory to a hydrogen molecule embedded in twelve membered boron cluster (B(12)) in excited states, which are densely quasi-degenerate due to the vacancy in 2p orbitals of boron atom [1s(2)2s(2)2p(1)]. Bond dissociation of the hydrogen molecule quickly takes place in the cluster and the resultant hydrogen atoms are squeezed out to the surface of the cluster. We further study collision dynamics between H(2) and B(12), which also gives interesting phenomena. The present study suggests an interesting functionality of the boron clusters.
我们发展了一种理论及其应用方法，用于研究在分子几何形状广泛范围内绝热势能超曲面（PES）密集准简并的体系中的化学动力学。在这些绝热电子态中，强非绝热相互作用往往会使它们彼此耦合。因此，从技术上讲，在这些体系中准确地单独挑选出各个 PES 通常是极其困难的。此外，由于相互非绝热耦合可能在空间中广泛传播，并且由于能量-时间不确定性关系，孤立且明确的势能面的概念将失去意义。另一方面，这种密集的电子态应该提供一个非常有趣的分子场，其中化学反应以特征方式进行。然而，为了处理这些体系，化学反应动力学的标准理论框架，从 Born-Oppenheimer 近似开始，以量子核波包动力学结束，并不是很有用。我们在这里使用我们开发的非绝热电子波包理论来探索这个问题，我们称之为相空间平均和自然分支（PSANB）方法[T. Yonehara 和 K. Takatsuka，J. Chem. Phys. 129, 134109（2008）]，或分支路径表示，其中波包沿着非 Born-Oppenheimer 分支路径随时间传播。在本文中，在概述基本理论之后，我们使用一维模型检查 PSANB 方法在这种密集准简并非绝热体系中的工作效果。为此，我们将 PSANB 的性能与全量子力学结果以及少数开关表面跳跃（FSSH）方法的结果进行比较，后者是迄今为止最可靠和灵活的方法之一。事实证明，PSANB 电子波包方法实际上可以用更少的初始采样路径得到非常好的结果。然后，我们将电子波包动力学应用于分支路径表示和所谓的半经典 Ehrenfest 理论，研究嵌入在十二元硼团簇（B(12)）中的处于激发态的氢分子，由于硼原子 2p 轨道中的空位，这些氢分子处于密集准简并状态[1s(2)2s(2)2p(1)]。氢分子在团簇中迅速发生键解离，生成的氢原子被挤出到团簇表面。我们进一步研究了 H(2)和 B(12)之间的碰撞动力学，这也产生了有趣的现象。本研究表明硼团簇具有有趣的功能。
