State Key Laboratory of Quantum Optics and Quantum Optics Devices, Institute of Laser Spectroscopy, Shanxi University, Taiyuan 030006, China.
Phys Chem Chem Phys. 2015 Nov 28;17(44):29421-64. doi: 10.1039/c5cp03982g. Epub 2015 Oct 19.
An elementary molecular process can be characterized by the flow of particles (i.e., electrons and nuclei) that compose the system. The flow, in turn, is quantitatively described by the flux (i.e., the time-sequence of maps of the rate of flow of particles though specified surfaces of observation) or, in more detail, by the flux density. The quantum theory of concerted electronic and nuclear fluxes (CENFs) associated with electronically adiabatic intramolecular processes is presented. In particular, it is emphasized how the electronic continuity equation can be employed to circumvent the failure of the Born-Oppenheimer approximation, which always predicts a vanishing electronic flux density (EFD). It is also shown that all CENFs accompanying coherent tunnelling between equivalent "reactant" and "product" configurations of isolated molecules are synchronous. The theory is applied to three systems of increasing complexity. The first application is to vibrating, aligned H2(+)((2)Σg(+)), or vibrating and dissociating H2(+)((2)Σg(+), J = 0, M = 0). The EFD maps manifest a rich and surprising structure in this simplest of systems; for example, they show that the EFD is not necessarily synchronous with the nuclear flux density and can alternate in direction several times over the length of the molecule. The second application is to coherent tunnelling isomerization in the model inorganic system B4, in which all CENFs are synchronous. The contributions of core and valence electrons to the EFD are separately computed and it is found that core electrons flow with the nuclei, whereas the valence electrons flow obliquely to the core electrons in distinctive patterns. The third application is to the Cope rearrangement of semibullvalene, which also involves coherent tunnelling. An especially interesting discovery is that the so-called "pericyclic" electrons do not behave in the manner typically portrayed by the traditional Lewis structures with appended arrows. Indeed, it is found that only about 3 pericyclic electrons flow, in contrast to the 6 predicted by the Lewis picture. It is remarkable that the time scales of these three processes vary by 18 orders of magnitude: femtoseconds (H2(+)((2)Σg(+))); picoseconds (B4); kilosceconds (semibullvalene). It is emphasized that results presented herein are appearing in the literature for the first time.
一个基本的分子过程可以通过组成系统的粒子（即电子和原子核）的流动来描述。这种流动反过来又可以通过通量（即通过指定观察表面的粒子流率的时间序列图）或更详细地通过通量密度来定量描述。本文介绍了与电子绝热分子内过程相关的协同电子和核通量（CENFs）的量子理论。特别是强调了如何利用电子连续性方程来规避玻恩-奥本海默近似的失效，该近似总是预测电子通量密度（EFD）为零。还表明，与孤立分子中等效“反应物”和“产物”构型之间的相干隧穿相关的所有 CENFs 都是同步的。该理论应用于三个越来越复杂的系统。第一个应用是振动的、对齐的 H2(+)((2)Σg(+))，或振动和离解的 H2(+)((2)Σg(+), J = 0, M = 0)。在这个最简单的系统中，EFD 图谱表现出丰富而令人惊讶的结构；例如，它们表明 EFD 不一定与核通量密度同步，并且可以在分子长度上多次改变方向。第二个应用是模型无机体系 B4 中的相干隧穿异构化，其中所有 CENFs 都是同步的。分别计算了芯和价电子对 EFD 的贡献，发现芯电子随原子核流动，而价电子以独特的模式斜向芯电子流动。第三个应用是半轮烯的 Cope 重排，其中也涉及相干隧穿。一个特别有趣的发现是，所谓的“周环”电子的行为方式与传统的带有附加箭头的路易斯结构所描述的方式不同。事实上，发现只有大约 3 个周环电子流动，而路易斯图像预测有 6 个。值得注意的是，这三个过程的时间尺度相差 18 个数量级：飞秒（H2(+)((2)Σg(+))）；皮秒（B4）；千秒（半轮烯）。强调的是，本文呈现的结果是首次出现在文献中。
