Visualization of static Jahn-Teller effects in the fullerene anion ${\text{C}}_{60}^{-}$

Adsorption of ${\text{C}}_{60}$ on a metallic surface may be expected to result in electronic charge transfer to the organic adsorbant, even if a buffer layer is included between the ${\text{C}}_{60}$ molecules and substrate. Subsequently, intramolecular coupling between the molecule’s electronic and vibrational degrees of freedom would be expected to result in species subject to Jahn-Teller (JT) distortions. In this work, we use Hückel molecular-orbital theory to visualize the effect that JT interactions may have on ${\text{C}}_{60}^{-}$ ions imaged using scanning tunneling microscopy (STM). Several distortion symmetries and adsorption orientations are considered and the resulting simulations are compared to STM images in the literature.

Figure 1

(Color online) Definition of the adsorption angle $\varphi$. The black square (at $\varphi =0$ here) represents the region of space scanned by the STM tip, so the surface is parallel to it but on the opposite side of the molecule. The labels $\text{C}n$ are used to denote $n$-fold symmetry axes.

Figure 2

(Color online) The electron distribution associated with the fully degenerate LUMO of ${\text{C}}_{60}$. (a) shows that the electrons are localized on the pentagonal faces, and (b) shows a high-resolution STM simulation for an ion adsorbed with a $C_2$ axis normal to the surface in the absence of JT and surface interactions.

Figure 3

(Color online) Pictorial representation of the electronic coordinates of the wells of (a) $D_{5d}$, (b) $D_{3d}$, and (c) $D_{2h}$ symmetries. The nonbarred letters (blue online) correspond to the wells labeled as in Table and their inverted counterparts are distinguished using an overbar (red online). The surfaces shown are intended to convey an indication of the potential energy of the system corresponding to those electronic states.

Figure 4

The effect on the surface interaction energy for each $D_{5d}$ well of varying the adsorption angle $\varphi$.

Figure 5

High-resolution STM simulations of molecules locked into different $D_{5d}$ wells. The absorption orientation is indicated by the axis label ($C_2$, etc.) which indicates which axis is normal to the surface, and an asterisk indicates the (degenerate) excited states.

Figure 6

The effect on the surface interaction energy for each $D_{3d}$ well of varying the adsorption angle $\varphi$.

Figure 7

High-resolution STM simulations of molecules locked into different $D_{3d}$ wells. The absorption orientation is indicated by the axis label C2, etc., which is normal to the surface.

Figure 8

The effect on the surface interaction energy for each $D_{2h}$ well of varying the adsorption angle $\varphi$.

Figure 9

High-resolution STM simulations of molecules locked into different $D_{2h}$ wells. The absorption orientation is indicated by the axis label ($C_2$, etc.) which is normal to the surface. As the excited states are not generally degenerate, but may be close, images are drawn showing the states both on their own and when degenerate (labeled “deg.”). Single and double asterisks indicate the states as ordered in Table , e.g., ${\mathsf{A}}^{\ast }=\left(1,0,0\right)$ and ${\mathsf{A}}^{\ast \ast }=\left(0,1,0\right)$.

Figure 10

(Color online) Experimental STM images of ${\text{C}}_{60}$ molecules on an alkylthiol SAM on Au(111), reprinted from part of Fig. 2 of Ref. 27 with permission from Macmillan Publishers Ltd, Copyright (2001). The insets show their suggested molecular orientations. To the right are possible matches taken from our STM simulations of JT-distorted ${\text{C}}_{60}^{-}$ ions.

Figure 11

Experimental STM images of ${\text{C}}_{60}$ molecules on an alkylthiol SAM on Au(111), reprinted from Fig. 1 of Ref. 28 with permission from American Chemical Society, Copyright (2003). The authors’ simulations are shown inset into each image. Below are possible matches taken from our STM simulations of JT-distorted ${\text{C}}_{60}^{-}$ ions.

Figure 12

STM images of ${\text{C}}_{60}$ molecules on Au(111), reproduced from Ref. 31. The images were observed at a sample bias of 2 V with relative abundances (a) 38%, (b) 35%, (c) 13%, (d) 8%, and (e) 6%. The latter three images are very similar to those expected from differently oriented $D_{5d}$-distorted anions, as shown along the bottom of the figure.

Figure 13

High-resolution STM image of a spray deposited ${\text{C}}_{60}$ monolayer on Au(111), reprinted from part of Fig. 3 of Ref. 34 with permission from the Institute of Physics. The experimental image was recorded at 5 K using a sample bias of 2.5 V. The individual molecular images are very similar to those expected from a $D_{5d}$-distorted anion adsorbed with a $C_2$ axis prone to the surface, as shown on the right of the figure.

Figure 14

(Color online) (Top) Experimental STM images of a nominally ${\text{K}}_4{\text{C}}_{60}$ monolayer on Au(111) recorded at biases slightly above and below the Fermi energy ($E_{\text{F}}$; $T=7\text{K}$), and (middle) DFT simulations of a $D_{2h}$-distorted ${\text{C}}_{60}^{4-}$ ion, reprinted from parts of Figs. 3 and 4 of Ref. 6 with permission from AAAS. (Bottom) Our STM simulations of a set of nondegenerate $T_{1u}$ orbitals, where $x\equiv T_{1ux}$, etc. At the very bottom, the arrows represent HMO occupancy and all simulations assume a $C_2$ axis is normal to the surface.

Figure 15

STM image of a ${\text{C}}_{60}$ monolayer on Ag(001) adapted from Ref. 39. The tunneling parameters used were 2 V bias and 1 nA tunneling current $\left(T=7\text{K}\right)$. The BD contrast is clearly visible.

Figure 16

The two left-hand images are reprinted from parts of Fig. 2 of Ref. 45 with permission from Elsevir, Copyright (2000). Uppermost is an experimental STM image of a ${\text{C}}_{60}$ molecule adsorbed onto $\text{Si}\left(111\right)\text{−}\left(7\times 7\right)$ and below that is a HOMO-derived orbital calculated using local-density approximation-DFT. The labels c and g are retained from the original work. The two right-hand images are our LUMO-derived STM simulations of a $D_{5d}$-distorted ${\text{C}}_{60}$ anion adsorbed with a pentagonal face prone to the surface. The upper image simulates a high-resolution STM image and the lower image simulates the image that would be obtained with a 22-fold reduction in current.

Figure 17

(Color online) Regions of $D_{5d}$, $D_{3d}$, and $D_{2h}$ symmetries for the $T\otimes h$ JT problem.