Jahn-Teller effect in the cubic fullerides A₃C₆₀

Compared to isolated C₆₀³⁻ ions, characterized by a three-dimensional equipotential trough at the bottom of the lowest adiabatic potential energy surface (APES), the Jahn-Teller (JT) effect in cubic fullerides is additionally influenced by the interaction of JT distortions at C₆₀ sites with vibrational modes of the lattice. This leads to modification of JT stabilization energy and to the warping of the trough at each fullerene site, as well as to the interaction of JT distortions at different sites. Here we investigate these effects in three fcc fullerides with A = K, Rb, Cs and in Cs₃C₆₀ with bcc (A15) structure. DFT calculations of orbital vibronic coupling constants at C₆₀ sites and of phonon spectra have been done for fully ordered lattices (1 C₆₀/u.c.). Based on them the elastic response function for local JT distortions has been evaluated and the lowest APES investigated. To this end an expression for the latter as a function of trough coordinates of all sites has been derived. The results show that the JT stabilization energy slightly increases compared to an isolated C₆₀³⁻ and a warping of the trough of a few meV occurs. The interaction of JT distortions on nearest- and next-nearest-neighbor fullerene sites is of similar order of magnitude. These effects arise first of all due to the interaction of C₆₀ sites with the displacements of neighbor alkali atoms and are more pronounced in fcc fullerides than in the A15 compound. The results of this study support the picture of weakly hindered independent rotations of JT deformations at C₆₀ sites in cubic A₃C₆₀.

与孤立的C₆₀³⁻离子相比，后者在最低绝热势能面（Adiabatic Potential Energy Surface, APES）的底部呈现三维等势槽；立方富勒烯中的姜-泰勒（Jahn-Teller, JT）效应还受到C₆₀位点处JT畸变与晶格振动模式之间的相互作用影响。这将改变JT稳定能，使得每个富勒烯位点处的等势槽产生翘曲，同时还会引发不同位点间JT畸变的相互作用。本文针对A为K、Rb、Cs的三种面心立方（face-centered cubic, fcc）富勒烯，以及具有体心立方（body-centered cubic, bcc，即A15）结构的Cs₃C₆₀，对上述效应展开研究。我们针对完全有序的晶格（每个晶胞含1个C₆₀分子，即1 C₆₀/u.c.），开展了C₆₀位点处轨道-电子振动耦合常数以及声子谱的密度泛函理论（Density Functional Theory, DFT）计算。基于上述计算结果，我们评估了局域JT畸变的弹性响应函数，并对最低绝热势能面展开了研究。为此，我们推导了将最低绝热势能面表示为所有位点等势槽坐标函数的表达式。结果表明，相较于孤立的C₆₀³⁻离子，JT稳定能略有提升，且等势槽会出现数毫电子伏特（millielectronvolt, meV）量级的翘曲。相邻及次相邻富勒烯位点上的JT畸变之间的相互作用具有相近的数量级。上述效应主要源于C₆₀位点与相邻碱金属原子位移之间的相互作用，且该效应在面心立方富勒烯中比在A15结构化合物中更为显著。本研究结果支持“立方相A₃C₆₀中C₆₀位点处的JT形变可进行弱受限的独立旋转”这一观点。