Chemistry Reference
In-Depth Information
but no silogen-silogen interactions (because of the possible multiple placement
on a single site). Conversely, the hand-shake term
H
MD=TB
only contains
classically computed terms (SW interactions), and it includes all of the SW
pair interactions between a silogen and either a Si in the MD region or another
silogen, and all SW three-body interactions between at least one MD silicon
and a silogen-silicon pair. When computing the forces, all of the classical
and TB forces acting on the same atom are added together.
Lastly, it is worthwhile noticing that the Hamiltonian given in Eq. [26] is
conservative if the TB region is fixed, i.e., no dynamical allocation of the
region is employed. However, a dynamical allocation of such a region may
be extremely useful, for instance, in crack-propagation studies. A description
of how this could be achieved is beyond the scope of this review, and we refer
the interested reader to the original papers.
Learn on the Fly
The ''learn-on-the-fly'' (LOTF) method, suggested by Cs
´
nyi et al. in
2004,
75,265-267
tackles the question of how to seamlessly couple different
levels of theory in a way that is very different from everything we have exam-
ined up to this point. The method is constructed to join classical and quantum
mechanical descriptions inside a dynamical simulation. The significant novelty
of this approach is the fact that the focus is directly on the evaluation of the
forces acting on each atom in the system, instead of on the matching of differ-
ent Hamiltonians or on the constructing of a unique Hamiltonian containing
the different levels of theory. In addition, the method calls for a local refitting
of the classical parameters ''on the fly,'' i.e., during the course of each simula-
tion, to locally reproduce the quantum forces. This method could be seen as an
evolution of the ''serial'' approach discussed at the beginning of the chapter
(a higher level theory is used to determine parameters for a lower level theory
calculation), in which the concurrent application of different levels of theory,
the signature of hybrid approaches, enters through the evaluation of ab initio
data, which occurs while the simulation is running, is repeated every so many
time steps, and is local to each atom.
More specifically, this methodology employs molecular dynamics (MD)
(i.e., classical simulations) to investigate the dynamical evolution of the
system. However, instead of computing the forces acting on each atom from
a predefined classical potential, as in standard MD, the parametrization of
the potential is refitted every few time steps. This is accomplished using a
predictor-corrector scheme. At the beginning of the simulation, a well-behaved
potential is chosen, such that the equilibrium configuration of the system is
well reproduced. Then, during the predictor part of the scheme, the classical
forces acting on the atoms are computed using the parametrization given at
that time (
a
0
), and the system is evolved along the classical trajectories for a
few time steps, moving from
R
0
to
R
0
in phase space. At this point, the classical
and the quantum forces acting on the atoms at point
R
0
are computed
