T_(1u)h_g杨-泰乐系统:D_(5d)势阱中的各向异性现象

The anisotropic phenomena in the D_(5d) minima for the T_(1u)h_g Jahn-Teller system

杨 泰乐 (Jahn Teller缩写为JT)系统在其最低的绝热势能面上常常典型地含有一系列相互等同的势阱 .在C6 0 分子中 ,若一个电子占据该分子的三重简并的能量最低电子态 ,这一具有T1u 对称性的电子态将会与具有hg 对称性的五重简并振动态发生相互作用 ,形成所谓的T1u hgJT系统 .当考虑电声的非线性相互作用时 ,该系统的势能面上将出现D5d对称性的势阱并伴随D3d对称性的势垒 ;反之亦然 .本文在幺正平移变换的基础上 ,引入了标度变换 ,研究了该JT系统中D5d势阱中的各向异性现象 :在电子空间中 ,非线性项的引入使得阱中的能级分裂 ,通过计算 ,得到了阱中各能级的对称性及其相应的能量表达式 ;在电声耦合强度有限的情况下 ,利用幺正平移和标度变换 ,对阱中的能级分裂、声子的重叠积分以及能级的反演分裂都进行了计算 .其结果不仅展示了各向异性效应对系统中以上各物理量的影响 ,且对C6 0 分子的阴离子态C-6 0

Jahn Teller (JT) systems contain typically a set of mutually equivalent energy minima in the lowest adiabatic potential energy surface. When one electron occupies the three degenerate electronic states in C 60 molecules, the electronic states with a symmetry of T 1u and the five degenerate vibrational states with a symmetry of h g will be interacted and form the T 1u h g JT system. When the non linear vibronic interaction is considered, the JT system will contain the D 5d minima and D 3d maxima, and vice versa. In this paper, on the basis of unitary shift transformation, the modified scale transformation is introduced and the anisotropic phenomenon is studied in the D 5d minima for the T 1u h g JT system. The results are incorporated into the expressions for the states in the D 5d wells and their associate energies. The symmetries and their corresponding energies in the D 5d wells in the electronic space are obtained. For finite couplings, the phonon overlap between wells and inversion splitting are also studied. The results obtained in this paper not only show that the anisotropic effect has a significant influence on the above physical quantities, but also are of interest in the studies of anion states (C - 60 ) of the C 60 molecules and other C 60 anion related materials.