PdY_4团簇的电子-振动耦合及其杨-泰勒畸变的群论分析与Mathematica应用

An Analysis of the Vibronic Coupling and Jahn-Teller Distortion for PdY_4 Clusters Using Group Theory and Mathematica Application

利用群论和量子理论研究了具有C4v对称性构型的PdY4团簇的电子-振动耦合及其杨-泰勒畸变等问题.文中首先探讨了PdY4团簇的振动态对称性及其红外、拉曼活性,随后分析了PdY4团簇的电子-振动耦合以及振动-振动耦合,并借助Mathematica程序计算了振动-振动耦合的CG系数,最后利用群论进一步研究了PdY4团簇的杨-泰勒畸变.研究发现,PdY4团簇存在4种振动态,它们分别具有C4v群下的a1、b1、b2与e对称性,振动态a1和e同时具有红外与拉曼活性,而振动态b1和b2则只具有拉曼活性;在PdY4团簇的振动态中只有b1、b2是活跃的振动态;系统的电子-振动耦合将会导致系统发生杨-泰勒畸变,系统E←b1与E←b2的杨-泰勒畸变方向都是C4v→C2v,而E←(b1+b2)系统的杨-泰勒畸变方向则是C4v→C2.

The vibronic coupling and Jahn-Teller distortion of PdY4 clusters with C4v symmetry configuration are studied using group theory and quantum theory in this paper. In the first place, the symmetries of vibration states for PdY4 clusters are studied, and the infrared and Ramam activities of the vibration states for the cluster are discussed. In the second place, the vibronic coupling and the active vibration states of PdY4 clusters are analysed, the vibration-vibration couplings of PdY4 clusters are studied, and the CG coefficient of the e - e vibration coupling is computed using Mathematica program. In the final place, the Jahn-Teller distortion directions of PdY4 clusters are further studied using group theory. The results show： PdY4 clusters have four kinds of vibration states, they have the symmetries of al, bl, b2 and e under the group C4v. The vibration states a l and e refer to infrared and Ramam activities, the vibration states bl and b2 only refer to Ramam activity. Among the vibration states of PdY4 clusters, only the vibration states b l and b2 are the active vibration states. The coupling between the vibration state e and e should generate the coupling vibration states at, b1 and b2. The Jahn-Teller distortion of systems should occur because of the vibronic couplings, the Jahn-Teller distortion directions of the E b1 and E b2 systems are C4v→ C2v, and the Jahn-Teller distortion direction d the E （b1 ＋ b2） system is C4v → C2.