C_4^(2+)分子:T_2t_2系统的杨-泰勒畸变与各向异性现象的群论分析

Analysis on the Jahn-Teller Distortion and Anisotropic Phenomena of the T_2t_2 System for C_4^(2+) Molecules using Group Theory

依据群论与量子理论研究了C24+分子的T2t2系统的杨-泰勒畸变与各向异性现象.研究表明,C24+分子的电子基态具有Td群下的E、T1或者T2对称性,C24+分子一共存在3种不同的声子态a1、e与t2,其中只有e、t2是C24+分子的活跃声子态.借助投影算符导出了t2-t2声子耦合中的耦合声子态e的CG系数计算公式,并由此求出了CG系数值.进一步的研究发现:系统的杨-泰勒畸变导致C24+分子从Td对称性降低到C3v对称性;畸变致使C24+分子的三重简并的电子基态能级T2发生分裂;畸变同时还导致C24+分子的振动频率发生分解,而频率的分解就意味着C24+分子在空间上的各向同性遭到破坏而呈现出各向异性.

Jahn-Teller distortion and anisotropic phenomena of the T2 t2 system for C2^4＋ molecules were studied based on group theory and quantum theory. It was found that the ground electronic states of C2^4＋ molecules is E or T1 or T2 under the group Ta, the phonon states of C2 ＋ molecules are a1 and e and t2, only the phonon states e and t2 are the active phonon states of the system. The CG coefficient formulas of the coupling among phonon states t2 were derived u- sing the projection operators, and these CG coefficient values could be calculated further using the formulas obtained. Jahn-Teller distortion could cause that the symmetry of C2^4＋ molecules is lowered to C3v, from Ta and the ground energy level of the system is split into two energy levels. Moreover Jahn-Teller distortion could also cause the splitting of the vibrational frequency of the system, the frequency splitting means that the isotropy of C2^4＋ molecules was destroyed and the anisotropy of C2^4＋ molecules should appear after the Jahn-Teller distortion.