Origin of nanomechanical motion in a single-C${}_{60}$ transistor

We present a van der Waals density functional study of a negatively charged C${}_{60}$ on a Au(111) surface to investigate the nanomechanical motion in a single-molecular transistor [Park et al., Nature 407, 57 (2000)]. We found that the position of C${}_{60}$ is shifted away from the electrode surface when C${}_{60}$ is negatively charged because of the larger contribution from the Pauli repulsion between C${}_{60}^{-}$ and substrate than that from the attractive interaction with the image charge induced in the substrate. Implication to the Franck-Condon blockade is also discussed.

Figure 1

Interaction energies of C${}_{60}$ and C${}_{60}^{-}$ with the Au(111) surface as functions of molecule-surface distance. The molecule-surface distance is defined as the difference between the average $z$ coordinates of surface Au atoms and bottom C atoms of C${}_{60}$ (arrows in the inset). The energies in the vicinity of their equilibria are magnified and are shown in the inset.

Figure 2

Interaction energy curves for Li@C${}_{60}$ [$E_{\text{int}}(\text{Li}@{\text{C}}_{60}/\text{Au})$], that with image potential correction [$E_{\text{int}}(\text{Li}@{\text{C}}_{60}/\text{Au})-E_{\text{image}}\left(\text{Li}\right)$], and that with image potential correction and energy shift [$E_{\text{int}}(\text{Li}@{\text{C}}_{60}/\text{Au})-E_{\text{image}}\left(\text{Li}\right)-\Delta E$].

Figure 3

(a) Density of states projected onto C${}_{60}$ molecular orbitals (PDOS) and (b) crystal orbital overlap population (COOP) of C${}_{60}$ molecular orbitals with Au(111) substrate for the neutral state at the equilibrium distance ($Z_{\text{C}}=0.243$ nm). (c) PDOS and (d) COOP for the negatively charged state at the equilibrium ($Z_{\text{C}}=0.247$ nm). Energy is relative to the Fermi level ($E_{\text{F}}$).