Chemistry Reference
In-Depth Information
atomic-level resolution. Therefore, the avenue most commonly explored to
bypass such an impasse is the use of
hybrid methodologies
. Here, different
length scales are simulated simultaneously in a coupled fashion. The main
obstacle to overcome when producing such a hybrid simulation method is
developing an efficient and physically correct coupling scheme. Hybrid meth-
odologies, coupling schemes, and applications will be discussed in detail in the
next section.
A related topic is the issue of time scales. Dynamic simulations of atomic
behavior generally require time steps that are short enough to capture the
vibrational modes of the system, whereas changes at the macroscopic scale
usually occur over vastly longer time scales. Coupling between such widely
varying time scales is a very important challenge, but it is not within the scope
of this review. However, the problem of multiple-time-scale simulations will
be discussed briefly in the discussion of dynamical methods.
The need for coupled methodologies is definitely not limited to the phy-
sics of the solid state, and the subject has a long history. The first application
of hybrid methods to the solid state are the works of Gehlen et al.
26
and
Sinclair,
27
where continuum elasticity was used to provide realistic boundary
conditions for atomistic simulations. However, only recently, hybrid meth-
odologies have become widespread in solid-state physics, primarily because
of the explosion of interest in nanotechnology. Coupled methods have been
a key investigation technique for quite some time in many other fields as
well. In chemistry, for instance, combining quantum mechanics (QM) and
molecular mechanical (MM) potentials was started by Warshell and Levitt
in 1976
28
and has been common practice ever since. Several reviews of hybrid
QM/MM methods can be found.
29-32
However, these methodologies are not
necessarily well suited for studying many of the materials of interest in the
solid state, metals in particular. This is because QM/MM methods are
designed for covalently bonded organic molecules, i.e., materials where the
bond is strongly localized, while in metals bonds are strongly delocalized.
Hybrid methodologies have also been extensively applied to the investigation
of fluid behavior. In this field, we find extensive use of static coupling between
continuum and atomistic regimes, as in the Navier-Stokes/Monte Carlo
method of Dejong et al.
33
or Garcia et al.,
34
or the coupling of Monte Carlo
to fluid simulations proposed by Sommerer et al.
35
and Bogaerts et al.,
36
just to mention a few. Even more coupling schemes have been developed
to explore the dynamics of fluids. Among many, we want to mention the
continuum-to-molecular dynamics methods developed by O'Connell et al.,
37
by Hadjiconstantinou and Patera,
38
Hadjiconstatinou,
39
by Li et al.,
40
and
more recently by Wang and He.
41
Hybrid methodologies based solely on the
exchange of fluxes have been proposed as well, such as those by Flekkoy
et al.
42,43
Magnetism,
44
electromagnetism,
45
toxicology,
46
biology, and so
on are just a few other examples of fields that currently make systematic use
of hybrid methodologies.
