5 Enabling Materials By Dimensionality: From 0D to 3D Carbon-Based. . .
153
using first-principles molecular dynamics based on density functional treatment of
the electronic motion [43].
While this conclusion is expected when using classical molecular dynamics,
whereby atoms are treated as hard spheres interacting through a pair-wise potential,
making this model not capable of treating out-of-equilibrium conditions where
bonds are breaking and forming, it is surprising when electronic motion is explicitly
treated from first-principles. However, a critical reassessment of the validity of
the BO approximation – that is the assumption that the electrons at every instant
collapse into their ground state configuration – suggests that the electronic and
nuclear motion are intimately intertwined, due to the short time scales involved in
the molecule-surface collision.
Indeed, computer simulations allowing electron hopping between several excited
states, calculated by time-dependent density functional theory (TDDFT), indicate
that C 60 cage breaking can indeed occur for impact KEs of the order of 35 eV.
Figure 5.10b shows the progressively higher-energy surfaces visited by the electrons
during the simulation of a fullerene molecule approaching the silicon surface.
Due to the high-energy impact occurring in the timespan of a few femtoseconds,
electrons cannot relax fast enough to the ground state relative to the instantaneous
configuration of the nuclei. Thus, the forces acting on the nuclei during molecular
dynamics simulation must be calculated on the pure adiabatic surfaces populated at
the present time step. These gradients can be very different from the BO ground
state ones, leading to a highly dissociative path. Therefore, the cage disruption
cannot be accurately modelled at the measured KE if not by adopting a nonadiabatic
description of the impact. A similar behaviour was observed in the case of fullerene
molecules breaking upon impact on copper surfaces: we found out that one needs to
include excited-state dynamics in the description of the system in order to accurately
describe the processes involved in the collision and correctly estimate the cage
rupture energy threshold [46].
Similarly to what occurs with semiconducting silicon surfaces, even in the case
of collision with copper surface, C 60 cage breaking is observed for KEs slightly
higher than 40 eV. Unfortunately, this KE is marginally too high for SuMBE. In
the experimental section, we have seen indeed that in order to synthesize graphene
islands, we need to raise the substrate temperature up to 645 ◦ C after the impact.
It is worth noticing that the significant computational requirements of excitedstate simulations prevent following the system’s dynamics on time scales much
larger than several hundred femtoseconds in a reasonable time frame. Thus, one
needs to go beyond first-principles simulations and use multiscale approaches to
model the chemical-physical processes underlying graphene growth. Rearranging
the atoms to synthesize graphene, C 60 high-energy impacts on Cu and cage breaking
are the first two steps towards graphene growth on the substrate. In particular,
the energy released in the impact is absorbed by the distortion of the surface and
dissipates via phonon excitations. The system quickly reaches a regime where
excited-state dynamics is quenched and its evolution, thus, can be followed by
methods based on the validity of the BO approximation, notably density functional
theory (DFT).
153
using first-principles molecular dynamics based on density functional treatment of
the electronic motion [43].
While this conclusion is expected when using classical molecular dynamics,
whereby atoms are treated as hard spheres interacting through a pair-wise potential,
making this model not capable of treating out-of-equilibrium conditions where
bonds are breaking and forming, it is surprising when electronic motion is explicitly
treated from first-principles. However, a critical reassessment of the validity of
the BO approximation – that is the assumption that the electrons at every instant
collapse into their ground state configuration – suggests that the electronic and
nuclear motion are intimately intertwined, due to the short time scales involved in
the molecule-surface collision.
Indeed, computer simulations allowing electron hopping between several excited
states, calculated by time-dependent density functional theory (TDDFT), indicate
that C 60 cage breaking can indeed occur for impact KEs of the order of 35 eV.
Figure 5.10b shows the progressively higher-energy surfaces visited by the electrons
during the simulation of a fullerene molecule approaching the silicon surface.
Due to the high-energy impact occurring in the timespan of a few femtoseconds,
electrons cannot relax fast enough to the ground state relative to the instantaneous
configuration of the nuclei. Thus, the forces acting on the nuclei during molecular
dynamics simulation must be calculated on the pure adiabatic surfaces populated at
the present time step. These gradients can be very different from the BO ground
state ones, leading to a highly dissociative path. Therefore, the cage disruption
cannot be accurately modelled at the measured KE if not by adopting a nonadiabatic
description of the impact. A similar behaviour was observed in the case of fullerene
molecules breaking upon impact on copper surfaces: we found out that one needs to
include excited-state dynamics in the description of the system in order to accurately
describe the processes involved in the collision and correctly estimate the cage
rupture energy threshold [46].
Similarly to what occurs with semiconducting silicon surfaces, even in the case
of collision with copper surface, C 60 cage breaking is observed for KEs slightly
higher than 40 eV. Unfortunately, this KE is marginally too high for SuMBE. In
the experimental section, we have seen indeed that in order to synthesize graphene
islands, we need to raise the substrate temperature up to 645 ◦ C after the impact.
It is worth noticing that the significant computational requirements of excitedstate simulations prevent following the system’s dynamics on time scales much
larger than several hundred femtoseconds in a reasonable time frame. Thus, one
needs to go beyond first-principles simulations and use multiscale approaches to
model the chemical-physical processes underlying graphene growth. Rearranging
the atoms to synthesize graphene, C 60 high-energy impacts on Cu and cage breaking
are the first two steps towards graphene growth on the substrate. In particular,
the energy released in the impact is absorbed by the distortion of the surface and
dissipates via phonon excitations. The system quickly reaches a regime where
excited-state dynamics is quenched and its evolution, thus, can be followed by
methods based on the validity of the BO approximation, notably density functional
theory (DFT).