Zeng Tao, Hickman Riley J, Kadri Aya, Seidu Issaka
Department of Chemistry, Carleton University , Ottawa, Ontario K1S5B6, Canada.
J Chem Theory Comput. 2017 Oct 10;13(10):5004-5018. doi: 10.1021/acs.jctc.7b00787. Epub 2017 Sep 26.
We derive expansion formulas up to arbitrary order in vibrational coordinates for the tetrahedral and octahedral vibronic Hamiltonians that involve T and E states, and t and e vibrations. These states feature both Jahn-Teller (JT) and pseudo-Jahn-Teller (pJT) effects, and the vibrations are the most JT and pJT active. We first derive the formulas for 92 problems of T and T symmetries involving up to two vibrational modes. The formulas can be easily generalized to problems of T, O, and O symmetries, as well as problems involving more than two vibrational modes. They can also be adapted to describe spin-orbit vibronic Hamiltonians of tetrahedral p-type problems. Overall, this work makes crucial preparations for future studies on vibronic coupling problems of tetrahedral and octahedral systems. Most importantly, a new, simple, modularized approach to construct vibronic Hamiltonians for a set of related problems, instead of particular problems one by one, is presented.
我们推导了涉及T和E态以及t和e振动的四面体和八面体振动电子哈密顿量在振动坐标下直至任意阶的展开公式。这些态同时具有 Jahn-Teller（JT）效应和赝 Jahn-Teller（pJT）效应，并且这些振动是最具JT和pJT活性的。我们首先推导了涉及多达两个振动模式的T和T对称性的92个问题的公式。这些公式可以很容易地推广到T、O和O对称性的问题，以及涉及两个以上振动模式的问题。它们还可以适用于描述四面体p型问题的自旋轨道振动电子哈密顿量。总体而言，这项工作为未来关于四面体和八面体系统振动电子耦合问题的研究做了关键准备。最重要的是，提出了一种新的、简单的、模块化的方法来构建一组相关问题的振动电子哈密顿量，而不是逐个构建特定问题的哈密顿量。
