Chemistry Reference
In-Depth Information
Classical Domain
Cluster Atom
Hand-Shake Atom
Atom Position in the
Classical Domain
Termination Atom (H)
Quantum Cluster
Figure 18
Schematic representation of the cluster termination procedure. When
computing the cluster energy, atoms in the classical domain (dashed circles) are not
included in the calculations: Some cluster bonds are therefore left unsaturated (dashed
lines). For each hand-shake atom (dashed white circles) that is not included, a
termination atom (gray circles) is added, with position determined by minimizing the
mean-square forces acting on the cluster.
by minimizing the mean square forces that are acting on the cluster. A more
detailed description of how these positions are determined can be found in
Refs. 268 and 269. Lastly, both
E
cluster
QM
and
E
cluster
CP
are defined as the respective
energies for the terminated cluster.
Once the classical and quantum energies are determined, the correspond-
ing atomic forces are calculated and used within a molecular dynamics scheme.
A velocity Verlet algorithm
277
is used for the time integration. For more details
on how the method is implemented within a parallel scheme, using the message
passing interface (MPI), we refer to the original paper.
268-270
Applications
This methodology has been used to investigate oxidation
processes of Si(100) surfaces.
268,269
It was also used to model graphene
behavior,
278
and environmental effects of H
2
O on fracture initiation in
Si.
279
Lastly, in 2004, the methodology was expanded to allow for the
simulation of alumina systems.
280
In particular, it was used to study stress
corrosion cracking of
a
Al
2
O
3
.
Transparent Interface Method by Cheng et al.
As a last example of coupling mechanisms between quantum mechani-
cally described regions and classically modeled ones, we want to mention
the transparent interface method developped by Cheng et al.
281-283
This meth-
od was developed to model silicon dioxide, but it can easily be generalized to
describe different systems. In this methodology, a Born-Oppenheimer DFT
molecular dynamics (BO-DFT-MD) approach is considered, i.e., quantum
forces are used to drive molecular dynamics.
284
Also, such a methodology is
designed to cover the whole span from continuum to quantum. However, in
this review we are only going to present their quantum-to-classical coupling
approach, while we refer the reader interested in their description of the
continuum-to-classical treatment to the more specific studies listed above.
