基于C_4^（2+）分子的Tt_2系统的频率约化矩阵计算  

CALCULATION OF REDUCED MATRICES OF VIBRATIONAL FREQUENCIES OF THE Tt_2 SYSTEM FOR C_4^(2+) MOLECULES AND MATHEMATICA APPLYING

作　　者：王仙枝[1] 冯胜奇[2] 

机构地区：[1]韩山师范学院数学与信息技术系,广东潮州521041 [2]韩山师范学院物理与电子工程系,广东潮州521041

出　　处：《井冈山大学学报（自然科学版）》2012年第3期21-25,共5页Journal of Jinggangshan University (Natural Science)

基　　金：广东省自然科学基金项目(34613)

摘　　要：利用群论和微扰论计算了C42+分子的T?t2系统在其4个具有C3v对称性势阱中的频率约化矩阵。文中首先探讨了任意的杨-泰勒系统的频率约化矩阵及其计算方法,随后借助Mathematica程序求出了T?t2系统在其4个对称性势阱中的频率约化矩阵,最后利用群论进一步分析了系统的振动频率分解与各向异性现象。结果表明,系统的杨-泰勒畸变导致系统的三重简并振动模式t2的振动频率发生了分解,而系统的频率分解就意味着系统的各向同性遭到破坏而呈现出各向异性现象。The reduced matrices of vibrational frequencies of the T ？ t2 system for C42＋ molecules are calculated using group theory,perturbation theory and Mathematica program.Firstly,the reduced matrices of vibrational frequencies of the Jahn-Teller systems and their calculation methods are discussed.Furthermore,the reduced matrices of vibrational frequencies of the T ？ t2 system in the four minima are computed using Mathematica program.Finally,the phonon splitting and anisotropy of the system are further analyzed using group theory.It is found that the Jahn-Teller distortion results in phonon splitting of the triply degenerate vibrational mode t2 of C42＋ molecules,and the phonon splitting signifies that the isotropy of the system is destroyed and its anisotropy should appear.

关 键 词：频率约化矩阵 MATHEMATICA 频率分解 各向异性 

分 类 号：O561.1[理学—原子与分子物理]