  We investigate the atomic and electronic structures of cyclooctatetraene
(COT) molecules on graphene and analyze their dependence on external gate
voltage using first-principles calculations. The external gate voltage is
simulated by adding or removing electrons using density functional theory (DFT)
calculations. This allows us to investigate how changes in carrier density
modify the molecular shape, orientation, adsorption site, diffusion barrier,
and diffusion path. For increased hole doping COT molecules gradually change
their shape to a more flattened conformation and the distance between the
molecules and graphene increases while the diffusion barrier drastically
decreases. For increased electron doping an abrupt transition to a planar
conformation at a carrier density of -8$\times$10$^{13}$ e/cm$^2$ is observed.
These calculations imply that the shape and mobility of adsorbed COT molecules
can be controlled by externally gating graphene devices.

Materials Science