Zeng Tao, Seidu Issaka
Department of Chemistry, Carleton University, Ottawa, Ontario K1S5B6, Canada.
Phys Chem Chem Phys. 2017 May 10;19(18):11098-11110. doi: 10.1039/c7cp01171g.
In this work, we derive general expansions in vibrational coordinates for the (E + A) ⊗ (e + a) vibronic Hamiltonians of molecules with one and only one C axis. We first derive the expansion for the lowest C symmetry. Additional symmetry elements systematically eliminate terms in the expansion. We compare our expansions with the previous results for two cases, the and the C (E + A) ⊗ e. The first comparison demonstrates the robustness, completeness, conciseness, and convenience of our formalism. There is a systematic discrepancy in the second comparison. We discuss the origin of the discrepancy and use a numerical example to corroborate our expansion. Our formalism covers 153 vibronic problems in 6 point groups. It also gives general expansions for the spin-orbit vibronic Hamiltonians of the p-type (E + A) ⊗ (e + a) problems.
在这项工作中，我们推导了具有唯一一条C轴的分子的（E + A）⊗（e + a）振动电子哈密顿量在振动坐标下的一般展开式。我们首先推导最低C对称性的展开式。其他对称元素会系统地消除展开式中的项。我们将我们的展开式与之前关于（E + A）⊗e和C这两种情况的结果进行比较。第一次比较展示了我们形式体系的稳健性、完整性、简洁性和便利性。第二次比较存在系统性差异。我们讨论了差异的来源，并通过一个数值例子来证实我们的展开式。我们的形式体系涵盖了6个点群中的153个振动电子问题。它还给出了p型（E + A）⊗（e + a）问题的自旋 - 轨道振动电子哈密顿量的一般展开式。
