Chemistry Reference
In-Depth Information
pseudoatom will generate a force on the real atom because of the range of the
classical potential. However, displacing the real atomwill not produce a force
on the pseudoatom because of the nearest-neighbor nature of the continuum
interactions. It is such a mismatch in the forces that results in the formation of
ghost forces.
For hybrid methodologies dealing with dynamical processes, the need to
connect different computational models creates a second, very significant, pro-
blem: Wave reflections may occur at the artificial boundary. Such a reflection
arises because of the mismatch in wave spectra between the regions; a classical
atomistic region, for instance, emits waves that are significantly shorter than
those that can be captured by a continuum finite-element (FE) region.
Depending upon how the coupling between computational methods has
been handled, different classes of hybrid methodologies can be defined. A pos-
sible classification is in terms of the nature of the hand-shake region: Is it a
sharp interface between the computational domains or an extended area (as
in the example above)? Methodologies can also be divided depending upon
how the energy functional is constructed, whether a single energy functional
is used for the whole system or a different functional is constructed for each
domain, in which case an iterative procedure is then used to find equilibrium.
Lastly, coupling methodologies can also be separated into adaptive refinement
methods and domain decomposition methods. Adaptive refinement methods
are coupling schemes where a single macroscale model is considered over
the whole system; such a model is more highly refined over the area of interest
than away from it. Conversely, domain decomposition methods employ a
macroscale model only far from the area of interest, while in the vicinity of
it they make use of an atomistic model. In this review, examples of all of these
approaches will be presented.
Complete-Spectrum Hybrid Methods
In this review, methods are divided into two main classes: methodologies
dealing with the coupling of classical atomistic simulations to continuum ones
and methodologies coupling classical atomistic models to quantum mechani-
cal formulations. However, it is important to mention that a few methods
have been designed to cover the whole span from the continuum to the quan-
tum scale. Examples of these methods are the
coupling of length scales
(CLS)
method of Abraham et al., the
orbital-free density functional theory—quasi-
continuum
method (OFDFT-QC), the method developed by Ogata et al.,
and the
transparent interface
method by Cheng et al. All of these methodolo-
gies will be discussed in this review, with each coupling scheme in its appro-
priate section, i.e., the part of the method that deals with continuum/atomistic
coupling will be presented in the Atomistic/Continuum Coupling section, and
the part dealing with classical/quantum coupling in the Classical/Quantum
Coupling section.
