Electronic Energy Levels of Weakly Coupled Nanostructures: ${\mathrm{C}}_{60}$-Metal Interfaces

A new approach based on density functional theory and the Anderson impurity model is developed to calculate charging energies and quasiparticle energy gaps of molecular systems weakly coupled to an environment. The approach is applied to ${\mathrm{C}}_{60}$ adsorbed on Au(111) and Ag(100) surfaces, resulting in electronic structures that are in excellent agreement with recent experiments. Image-charge screening effects on molecular orbital energies are found to be of similar magnitude for the two surfaces, but charge-transfer screening and spin fluctuations also affect the Ag case due to a partially occupied ${\mathrm{C}}_{60}$ orbital.

Figure 1

Charging energy of the ${\mathrm{C}}_{60}$ molecule as a function of the molecule-substrate distance. Dots are results of our constrained DFT calculations for ${\mathrm{C}}_{60}$ on Au(111) [similar results are obtained for ${\mathrm{C}}_{60}$ on Ag(100)], and the solid line is a simple estimate with a point image charge, taking the image plane to be 1 Å [13, 39] above the outermost atomic plane of the substrate.

Figure 2

PDOS of ${\mathrm{C}}_{60}$ on Ag(100) and Au(111): (a) standard LDA results (molecule placed at the relaxed distance), (b) LDA results (corrected by 0.3 eV) shifted by the $\mathrm{DFT}+\mathrm{\text{screened}}$ $U$ method described in the text, and (c) the total spectral function including $\mathrm{DFT}+U$ and our Anderson impurity model for charge-transfer screening.