T_d群的T_2矩阵表示及T_d对称性系统t_2-t_2声子间耦合的CG系数计算

T_2 Matrix Representations of Group T_d and the Computations of CG Coefficient of t_2-t_2 Phonons Coupling for Systems with T_d Symmetry

依据群论与配位场理论,利用对称性分析的方法和投影算符等数学工具首先计算了Td群下T2的矩阵表示.随后探讨了具有Td对称性系统的t2-t2声子间耦合的CG系数计算问题,导出了该系统t2-t2声子间耦合的CG系数计算公式,最后具体计算出了这些CG系数值.文中的计算方法简明而易行,并且易于推广到其它情形中,所得到的CG系数计算公式可以方便地进行数值处理或者用计算机程序计算.所有的这些研究工作和所得到的结果对研究具有Td对称性系统的杨-泰勒效应及其物理特性都是有重要意义的.

T2 is an irreducible representation for group Td,according to group theory and ligand field theory,using the methods of symmetry analyses and the mathematical tools of projection operators and so on,the matrix representations of T2 for group Tdare calculated at first.Afterwards,the CG coefficient of t2-t2 phonons coupling for systems with Td symmetry are studied,deriving the formulas of CG coefficient for t2-t2 phonon coupling.Finally,these values of CG coefficient are computed using the formulas obtained in this paper.The methods of calculation there are simple and convenient,therefore,they can be spread to other conditions.The formulas derived in this paper may be suitable to carrying through calculations of numerical value or processing by computer.All these works and results in this paper are very important for studying Jahn-Teller effect of systems with Td symmetry and its physics characters.