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Abstract
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 Hückel 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.
Highlights
As with the pentagon-prone case, we find that scanning tunnelling microscopy (STM) images arising from the lowest unoccupied molecular orbital (LUMO) when hopping between wells is taken into account can be composed from a linear combination of images of ψz2 and, where z refers to a C3-axis perpendicular to the surface and through the centre of a hexagon
The method we have used in the previous sections has been to calculate values for the normal mode coordinates Qγ that result in minimum-energy configurations for any given set of JT and surface interaction parameters, which requires minimizing the energy of the lowest eigenvalue of a 3 × 3 matrix with respect to five different variables
We have used Huckel molecular orbital (HMO) theory and a symmetry analysis to investigate the influence of a combination of surface interactions and the dynamic JT effect in a C−60 ion on the appearance of the ion in STM images
Summary
The LUMO of a C−60 ion is subject to a T1u ⊗ 8hg JT effect, where a T1u electronic state couples to eight different sets of hg vibrational levels. On the minimum-energy surface (for both the D5d and D3d cases), they can be written in terms of just two angles, θ and φ, having the usual definitions for spherical polar coordinates. These can be obtained from [15] after changing to our notation and converting to our definitions of Qθ and Q. A pictorial representation of the electronic states will be useful when we interpret our predicted STM images, in that section we will represent complete points and not the angular variation with the radial coordinate representing energy. As the states are normalized, the points will lie on the surface of a sphere
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