Chemistry Reference
In-Depth Information
Figure 17
The TB/MD handshake (HS) region. The interface between the TB domain
and the MD one runs across a line of atoms, whose properties are modified to ensure
stability of the TB region. More specifically, these atoms are silogens (gray circles) and
act as terminations for the TB cluster (solid circles). Si atoms in the MD region are
represented by open circles.
The coupling scheme is schematically represented in Figure 17. Because
of the nature of the quantum interactions, the total energy in the TB region
cannot be localized on specific bonds, which makes defining the forces in
the hand-shake region a nontrivial matter. In particular, it is not possible to
average the MD and TB bond contributions across the interface in a compu-
tationally efficient way, as was done for the FE/MD interface. This is because
the Hellman-Feynman theorem, which is at the basis of the TB force calcula-
tions, would not be applicable, and numerical derivatives of the electronic
coefficients with respect to the atomic coordinates would therefore be needed.
The coupling strategy is therefore different from the one employed in the FE/
MD case. Now, the interface between the regions is defined as the ensemble of
atoms that constitute the outer shell of the TB cluster, instead of simply being a
line in between atomic planes. These atoms are called
silogens
, to indicate that
their properties have been modified to make them suitable terminations for the
TB cluster. More specifically, they are hydrogenlike atoms described by TB
parameters that were fitted to reproduce the correct Si-Si bond length and
binding energy, and to generate forces within the cluster that remain physical
as the cluster itself is deformed. Also, the silogen atoms are constrained to sit
where MD silicon used to be and, if more than one dangling bond needs ter-
mination, multiple silogens are placed at the same site. More details on the
fitting procedure and placement criteria for the silogens can be found in the
original papers.
66,67,158-162
When computing the TB part of the Hamiltonian (
H
TB
in Eq. [26]), all of
the Si-Si and Si-silogen interactions within the cluster are taken into account,
