强耦合的动力学Jahn-Teller效应理论

本文讨论了强耦合情况的、即电子的静态畸变能量大于晶格或分子振动量子能量的情况的动力学Jahn-Teller效应。我们发展了一种适用于强耦合情况的微扰方法,在其中将本征值及本征函数依照电子振动耦合系数的倒数或振动量子能量与静态畸变能量之比展开成幂级数,具体讨论了O_h点群中的Г₈态,求得了电子振动能级。区别于弱耦合情况的特点主要在于:1)虽然并不发生静态畸变,但是振动模的简并性及频谱却都发生了变化;2)如果与电子相耦合的振动模是“调谐”的,则电子及晶格振动的集体运动模将出现,这个理论能被用来解释Weinstock等人所做的关于TcF₆及ReF₆的红外光谱以及Raman光谱的实验结果。

THEORY OF THE DYNAMICAL JAHN-TELLER EFFECT IN STRONG COUPLING

The dynamical Jahn-Teller effect has been treated in the case of strong coupling for which the static distortional energy of electrons is larger than the energy of a typical vibrational quantum. A perturbation method which applies to strong coupling is developed. The eigenfunction and eigenvalue are expanded as power series of the ratio of the vibrational quantum to the static distortional energy. We have dealt explicitly with the Jahn-Teller effect of the Г₈ state of an O_h point group; the energy levels of electronic-vibration system are obtained. The characteristics of strong coupling as compared with weak coupling are: 1) although no static distortion actually appears, the degeneracy and frequency spectra of vibrational modes are changed; 2) the collective modes of electronic-vibration system will appear, if the vibrational modes coupled to the electrons are "tuned". The theory is employed to interpret the experimental results obtained by Weinstock et al. on TcF₆ and ReF₆ from the infra-red and Raman spectra.