分子中的赝旋转：电子轨道三重态
Pseudorotations in Molecules: Electronic Orbital Triplets
摘要：
本文用拓扑和几何方法计算了八面体、四面体和二十面体分子电子三重态振动谱的赝转动部分。计算中考虑了杨-泰勒效应中固有的非平凡几何。结果表明，Jahn-Teller效应产生了一种几何，它与E.嘉当伪旋转谱对应于具有这种几何的基空间上的非平凡线丛上的联络拉普拉斯算子的谱。在全局上，这些等参子流形形成了S^4的一个全测地叶理，并且计算了这个叶理上这些联络拉普拉斯算子的谱流。
英文摘要：
Topological and geometrical methods are used to calculate the pseudorotational part of the vibronic spectrum for an electronic triplet of an octahedral, tetrahedral, or icosahedral molecule. The calculations take into account the nontrivial geometry inherent in the Jahn-Teller effect. It is shown that the Jahn-Teller effect gives rise to a geometry, which is related to the isoparametric geometry of E. Cartan. The pseudorotational spectra correspond to the spectra of connection Laplacians on nontrivial line bundles over base spaces with this geometry. Globally, the isoparametric submanifolds form a totally geodesic foliation of S^4 and the spectral flow of these connection Laplacians on this foliation is computed.
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