Chemistry Reference
In-Depth Information
investigating insulators and semiconductors but not metals because of the
''cluster'' approach used in the quantum mechanical part of the calculations.
This formulation and the quantum classical coupling are discussed below.
However, because their continuum-classical coupling is strongly related to
the CLS approach (discussed above), it is not individually presented in this
review, and we refer the interested reader to the original papers.
268-270
In this methodology, a single energy functional is defined for the whole
system (FE/CP/QM), and the part of the Hamiltonian related to the quantum
mechanics (QM) and classical potential (CP) domains is given by
X
N
m
i
2
v
i
þ
¼
ð
r
i
2
CP
=
QM system
Þ
½
67
H
E
pot
i
¼
1
where
N
is the number of atoms in the CP/QM system,
m
i
is their mass, and
v
i
is their velocity.
E
pot
is the CP
þ
QM potential energy, and in this approach it
is written as
E
cluster
QM
E
pot
¼
ð
r
i
2
cluster
þ
handshake
Þ
½
68
þ
E
CP
ð
r
i
2
classical domain
þ
handshake
Þ
because the quantum domain consists of an atomic cluster around the area of
interest, and the classical domain surrounds it. Hand-shake atoms comprise
the interface between this cluster and its classical surroundings, and Eq. [68]
indicates that both the cluster and the classical-domain energies depend upon
such atoms. Instead of evaluating
E
CP
directly, the authors expressed this term
as
E
CP
E
CP=QM system
CP
¼
ð
r
i
2
CP
=
QM system
Þ
½
69
E
cluster
CP
ð
r
i
2
cluster
þ
handshake
Þ
½
70
as suggested by Svensson et al.
271
and Eichler et al.
272
Therefore, this treat-
ment does not require the explicit partitioning of
E
pot
into a quantum and a
classical term, as is done, for instance, in the CLS method discussed above.
However, it does require the classical and quantum mechanical evaluation
of the cluster energy, as well as the classical evaluation of the energy of the
whole QM/CM system.
In both the classical and the quantum mechanical computations of the
cluster energy, it is necessary to terminate the cluster's dangling bonds, to
obtain a stable structure (see Figure 18). The use of H atoms is appropriate
when considering semiconductors or insulators.
273-276
The termination atoms
are placed instead of the hand-shake atoms, and their position is determined
