A general model for the analysis of the Adiabatic Potential Energy Surfaces (APES) of the molecules that are subject to the multimode Jahn–Teller effect is presented. The method utilizes the information obtained by DFT calculations on a distorted stationary point on the APES. The essence of the model is to express the distortion along a model minimal energy path called Intrinsic Distortion Path (IDP), projecting the geometry of the system on the normal modes of the either high-symmetry (HS) or low symmetry (LS) nuclear configuration. This allows us to determine the significance of all of the involved normal modes along a relevant particular path of distortion, and the direct calculation of the vibronic coupling constants. The IDP analysis is illustrated by the discussion of the multimode H ⊗ (g + 2h) JT effect in fullerene cations (C60+) giving a deep insight into the origin and the mechanism of vibronic coupling in fullerene based molecules.

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General treatment of the multimode Jahn–Teller effect: study of fullerene cations

The dynamical Jahn-Teller effect on fullerene sites in insulating ${\mathrm{Cs}}_{3}{\mathrm{C}}_{60}$ is investigated fully ab initio. The vibronic excitations of rotational type are at $\ensuremath{\ge}65\text{ }\text{ }{\mathrm{cm}}^{\ensuremath{-}1}$, while the net kinetic contribution to the Jahn-Teller stabilization energy constitutes approximately 90 meV. This means that no localization of distortions by intermolecular interactions is possible in these fullerides; therefore, free rotations of deformations take place independently on each ${\mathrm{C}}_{60}$. The latter destroy the orbital ordering and establish a conventional exchange interaction between $S=1/2$ on fullerene sites. The corresponding exchange model is derived and predicts the N\'eel temperature for A15 ${\mathrm{Cs}}_{3}{\mathrm{C}}_{60}$ close to experiment.

Dynamical Jahn-Teller effect and antiferromagnetism in Cs3C60.

Diffuse interstellar bands (DIBs) are puzzling absorption features believed to contain critical information about molecular evolution in space. Despite the fact that C60+ recently became the first confirmed carrier of several DIBs, the nature of the corresponding transitions is not understood. Using electronic structure methods, we show that the two strong C60+ DIBs cannot be explained by electronic transitions to the two different excited 2E1g states or the two spin–orbit components of the lowest 2E1g state, as suggested before. We argue that the strong DIBs at 9632 and 9577 A correspond to the cold excitations from the non-Franck–Condon region of the ground electronic state to the two components of the lowest 2E1g state split by Jahn–Teller distortion. The weak DIBs at 9428 and 9365 A are assigned to the first vibronic transitions involving the low-energy vibrational modes and components of the lowest 2E1g electronic state.

Electronic Transitions Responsible for C60+ Diffuse Interstellar Bands.

Fullerene molecules adsorbed on surfaces often show macroscopic average distortions. As charged ions C
 60
 are known to be Jahn-Teller (JT) active, it is suggested that these distortions could be a manifestation of cooperative JT effects (CJTE) due to interactions between neighbouring fullerene ions. In order to understand the distortion properties it is necessary to take correlations between different distortions into account. However, this can’t easily be done in the mean field approximation usually used to describe the CJTE. We therefore propose an alternative procedure to describe 2D mesoscopic islands of C60 ions in which a pseudo vector spin $$\vec S$$
 is evoked to represent degenerate JT-distorted states when the quadratic JT coupling is considered. This approach is analogous to methods used for 2D magnetic systems. We then use the differential operator technique in effective field theory within the Ising approach. We include the effects of weak surface interactions and dynamic motion between equivalent distortions via terms equivalent to anisotropy and a transverse field
in magnetism respectively. For distortions to D
 5d
 symmetry, we determine single site correlations as a function of temperature, the macroscopic average distortion describing a structural phase transition, and the isothermal response function. Phase diagrams are
presented for relevant cases of the system parameters.

Cooperative Jahn-Teller effect in a 2D mesoscopic C60n− system with D5d symmetry adsorbed on buffer layers using Ising EFT model

Using scanning tunnelling microscopy (STM), it is possible to observe detailed structure of the molecular orbitals (MOs) of fullerene anions C−60. However, understanding the experimental observations is not straightforward because of the inherent presence of Jahn–Teller (JT) interactions, which (in general) split the MOs in one of a number of equivalent ways. Tunnelling between equivalent distortions means that any observed STM image will be a superposition of images arising from the individual configurations. Interactions with the surface substrate must also be taken into account. We will show how simple ideas involving a symmetry analysis and Huckel molecular orbital theory can be used to understand observed STM images without need for the more usual but more complicated density functional calculations. In particular, we will show that when the fullerene ion is adsorbed with a pentagon, hexagon or double-bond facing the surface, STM images involving the lowest unoccupied molecular orbital (LUMO) can be reproduced by adding together just two images of squares of components of the LUMO, in ratios that depend on the strength of the JT effect and the surface interaction. It should always be possible to find qualitative matches to observed images involving any of these orientations by simply looking at images of the components, without doing any detailed calculations. A comparison with published images indicates that the JT effect in the C−60 ion favours D3d distortions.

Manifestation of dynamic Jahn-Teller distortions and surface interactions in scanning tunnelling microscopy images of the fullerene anion C 60

A study of the quadratic p2 ⊗ h Jahn–Teller system

A theoretical investigation of the pseudorotational dynamics in the ${\mathrm{C}}_{60}^{+}$ cation is made using a single-mode $H\ensuremath{\bigotimes}h$ model Analytical expressions for the rate of pseudorotation are formulated as a function of the vibronic coupling parameters and used to probe the dynamics of the Jahn-Teller effect For particular values of the coupling constants, it is known that the ground state of the system may change from the expected $H$ symmetry to one of $A$ symmetry Therefore, we examine the dynamics in the coupling regime where this ground-state $H$-$A$ crossover occurs Using coupling constants taken from the literature, a pseudorotational period of $\ensuremath{\sim}210\phantom{\rule{03em}{0ex}}\mathrm{fs}$ is estimated for this ion Thus there is the potential that pseudorotation could be observed in ultrafast optical experiments

Lubna M. Sindi

Papers

A study of the quadratic p2 ⊗ h Jahn–Teller system

Theoretical treatment of pseudorotation in the Jahn-Teller C 60 + ion