Takatsuka Kazuo, Arasaki Yasuki
Fukui Institute for Fundamental Chemistry, Kyoto University, 606-8103 Kyoto, Japan.
J Chem Phys. 2021 Mar 7;154(9):094103. doi: 10.1063/5.0034810.
We propose and numerically demonstrate that highly correlated electronic wavefunctions such as those of configuration interaction, the cluster expansion, and so on, and electron wavepackets superposed thereof can be analyzed in terms of one-electron functions, which we call energy natural orbitals (ENOs). As the name suggests, ENOs are members of the broad family of natural orbitals defined by Löwdin, in that they are eigenfunctions of the energy density operator. One of the major characteristics is that the (orbital) energies of all the ENOs are summed up exactly equal to the total electronic energy of a wavefunction under study. Another outstanding feature is that the population of each ENO varies as the chemical reaction proceeds, keeping the total population constant though. The study of ENOs has been driven by the need for new methods to analyze extremely complicated nonadiabatic electron wavepackets such as those embedded in highly quasi-degenerate excited-state manifolds. Yet, ENOs can be applied to scrutinize many other chemical reactions, ranging from the ordinary concerted reactions, nonadiabatic reactions, and Woodward-Hoffman forbidden reactions, to excited-state reactions. We here present the properties of ENOs and a couple of case studies of numerical realization, one of which is about the mechanism of nonadiabatic electron transfer.
我们提出并通过数值证明，诸如组态相互作用、团簇展开等高度相关的电子波函数，以及由它们叠加而成的电子波包，可以用单电子函数来分析，我们将这种单电子函数称为能量自然轨道（ENOs）。顾名思义，ENOs是由洛丁定义的广义自然轨道家族的成员，因为它们是能量密度算符的本征函数。其主要特征之一是，所有ENOs的（轨道）能量之和恰好等于所研究波函数的总电子能量。另一个显著特点是，随着化学反应的进行，每个ENO的布居数会发生变化，不过总布居数保持不变。对ENOs的研究是由分析极其复杂的非绝热电子波包（如那些嵌入高度准简并激发态流形中的波包）的新方法需求所推动的。然而，ENOs可应用于仔细研究许多其他化学反应，从普通的协同反应、非绝热反应、伍德沃德 - 霍夫曼禁阻反应到激发态反应。我们在此展示ENOs的性质以及几个数值实现的案例研究实例，其中一个是关于非绝热电子转移的机制。
