Abstract

The fullerene level diagram is analyzed using the molecular orbital theory. The interaction of π electrons due to their hopping between adjacent carbon atoms leads to the formation of collective states with the symmetry of a truncated icosahedron. The symmetry of the icosahedron group is shown to form an unusual spectrum of levels associated with the form of the angular part of wave functions. The irreducible representations of the rotation group of icosahedron are interpreted in terms of spherical functions. Formulas for the calculation of the excitation cross sections of electronic levels and the spontaneous relaxation time are presented. It is shown that these spontaneous relaxation times are orders of magnitude longer lived than the times of nonradiative relaxation, which arises due to the Jahn–Teller effect, because of spontaneous symmetry break upon interaction with the phonon spectrum. Because of fast nonradiative processes, despite the existence of an absorption spectrum, the emission spectrum in the optical region is not observed. Instead, thermal radiation is registered in the frequency range of the phonon spectrum. Methods to obviate the problem of quenching the electronic radiation spectrum are proposed.

中文翻译：

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二十面体的对称性和富勒烯C 60的光学性质

摘要

使用分子轨道理论分析了富勒烯能级图。π电子的相互作用是由于相邻碳原子之间的跳跃引起的，从而形成了具有截短二十面体对称性的集体态。二十面体群的对称性显示出形成了与波函数角部分形式相关的不寻常的能级谱。二十面体旋转群的不可约表示用球面函数解释。给出了计算电子能级的激发截面和自发弛豫时间的公式。结果表明，这些自发的弛豫时间比非辐射弛豫时间长几个数量级，这是由Jahn–Teller效应引起的，由于自发对称性，在与声子谱相互作用时会破裂。由于快速的非辐射过程，尽管存在吸收光谱，但未观察到光学区域中的发射光谱。而是将热辐射记录在声子频谱的频率范围内。提出了消除电子辐射谱淬灭问题的方法。