The
molecular hopping of a lone 3,4,9,10-perylenetetracarboxylic
dianhydride (PTCDA) molecule adsorbed on a Ge(001) surface is studied
by density functional theory calculations and the climbing-image nudged
elastic band method, in which the PTCDA molecule moves along a trough
between two adjacent Ge dimer rows. We confirm the previously reported
stable state (SS) structure and determine the transition state (TS)
structure during the hopping. The TS exhibits the following characteristic
features: PTCDA is almost flat above the surface and the adsorption
energy (−1.69 eV) is mostly due to the van der Waals (vdW)
interaction. The hopping rate constant calculated from the Gibbs free
energy of activation indicates that PTCDA is unlikely to hop at 500
K but likely to hop at about 700 K. From changes of Ge–O bond
distances during the hopping, the mechanism is named an “inchworm/cheetah”-like
hopping with concerted dimer flipping. The origin of the adsorption
energy changes from the chemical interaction plus the vdW interaction
at the SS to the vdW interaction at the TS during the hopping. The
present study gives an insight that strongly adsorbed planar molecules
with functional groups on reactive semiconductor surfaces are more
mobile than expected.