T1u×hg Jahn-Teller系统：D3d势阱中的频率分解与能级分裂

在C60分子中，未被填充的最低电子态具有T1u对称性，因此，对中性的C60而言，不论是通过分子内部激发，或是外部掺杂，都易被一个电子占据而形成Jahn-Teller（JT）活跃电子态.此态与五重简并的hg声子态耦合，构成所谓的T1u-hg -JT系统.在这一JT系统中，当只考虑电声的线性耦合时，其绝热势能面是一个槽形.但在实际的系统中，二阶电声耦合是存在的，理论研究表明，原来的势槽将被这二阶非线性耦合弯曲成D3d或D5d对称性的势阱.声子振动态在阱中将显示各向异性效应，使得声子沿不同的方向有不同的振动频率，进而影响势阱中的能级分布、势阱间的重叠积分，以及整个系统的隧道能级分裂等.对D3d势阱中各向异性效应进行了研究，利用幺正平移、?pik Pryce和标度变换等方法计算了系统势阱中的能级，以及阱中的振动频率，研究了势阱中的能级间隔以及微绕修正能量的变化，并由此导出了这些物理量在仅有线性耦合的势槽中变化的情形. 关键词： C60 Jahn-Teller效应 各向异性 电声耦合

The phonon and energy splitting in the D3d minima for the T1uhg Jahn-Teller system

In C60 molecules, the lowest unoccupied molecular orbital has T1u symmetry. The orbital is easily occupied by an electron through molecular inner excitation or doping and becomes an active Jahn-Teller (JT) electronic state. The T1u-hg- JT system is formed by the coupling of such an electronic state to a five-fold degenerate hg mode. The linear vibronic coupling in the system forms a trough on the adiabatic potential surface of the system, but D5d and D3d minima will be warped while considering the quadratic vibronic coupling. Phonon states in minima will have anisotropic effects and the vibrational frequencies should be different in different directions. This phenomenon will further affect the energy distribution, phonon overlap and tunneling effect in the system. The anisotropic effect is carefully studied in detail for D3d-minima. The energies and vibrational frequencies are calculated using unitary shift transformation, pick-Pryce method, scale transformation and energy minimization procedure. The energy gap and the variation of perturbation energy in minima are obtained in this paper and the same physical quantities in trough are derived through changing the values of the quadratic coupling constants.