Theoretical Modeling

STS spectra and images contain a lot of information about the nature of C₆₀ states, as well as the C₆₀-Ag(100) interaction. Using density functional theory calculations we can determine the extent to which substrate-C₆₀ bonding, charge transfer, and state hybridization work together to produce the observed electronic features.

Theoretical modeling also reveals the extent to which the C₆₀ topography affects the way STS dI/dV maps measure C₆₀ molecular states. The most common way to visualize theoretical maps of C₆₀ states is to plot surfaces of constant state density (state iso-surfaces). The state iso-surfaces for the C₆₀ LUMO and LUMO+1 states are shown in Figure 5. These maps, however, due not accurately depict the STS maps. This is not surprising since STS maps do not measure state density iso-surfaces, but rather they measure local state density over topographical contours. Mimicking the C₆₀ topography by a hemisphere and calculating state density on this contour still does not accurate reproduce the STS measurement, as seen in Figure 1.

Figure 1. Comparison of three different theoretical models of STS measurements of C₆₀ LUMO and LUMO+1 states.

The STS dI/dV maps are well reproduced once the true C₆₀ topography is taken into account. By calculating state density over the simulated STM tip trajectory (the theoretical topographs in Fig. 2), the remaining discrepancies are eliminated and a good match is achieved between theoretical and experimental maps.

Figure 2. Density functional theory computation of STS measurements of C₆₀ electronic structure.

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References

Charge transfer and screening in individual C₆₀ molecules on metal substrates: A scanning-tunneling-spectroscopy and theoretical study
Xinghua Lu, M. Grobis, K.H. Khoo, Steven G. Louie, and M. F. Crommie
Phys. Rev. B 70, 115418 (2004)

Energy Resolved Imaging of Fullerene Molecular Orbitals
M. Grobis, Xinghua Lu, K.H. Khoo, Steven G. Louie, and M. F. Crommie
Proceedings of the 12th International Conference on Scanning Tunneling Microsocopy/Spectroscopy and Related Techniques. AIP CP# 696, 20 (2003)

Spatially Mapping the Spectral Density of a Single C₆₀ Molecule
Xinghua Lu, M. Grobis, K.H. Khoo, Steven G. Louie, and M. F. Crommie
Phys. Rev. Lett. 90, 096802 (2003)