Chemistry Reference
In-Depth Information
CLASSICAL/QUANTUM COUPLING
Coupled methodologies that connect classically described domains to
quantum mechanically described regions encounter the same difficulties that
continuum-to-classical methods do (possible ghost forces at the artificial
boundary and phonon reflection when dynamics is taken into account). More-
over, the fact that using ab initio methods makes it impossible to localize the
energy onto specific atoms or bonds makes dealing with the hand-shake region
even more complicated. Furthermore, methods coupling atomistic to quantum
calculations also have to face problems related to dealing with the electronic
degrees of freedom in the quantum mechanical domain. In principle, the
presence of such degrees of freedom requires the imposition of boundary con-
ditions on the electronic wave function at the interface between the two
domains. Such a complication is particularly serious when dealing with metals
because of the nearly complete delocalization of the bonds. In the following,
we will explore how several methodologies have dealt with such issues in both
static and dynamical phenomena.
Static and Semistatic Methods
Orbital-Free DFT-Classical Mechanics
One approach to couple classically treated regions to regions described
by quantum mechanics is to use the methodology introduced by Choly et al.
241
in 2005. In this formalism, the quantum mechanical zone is modeled using
orbital-free density functional theory (OFDFT), which is an approximate
form of DFT where the kinetic energy of the noninteracting electrons is
approximated by a functional of the density.
242-246
This allows the energy
of the system to be expressed as the sum of terms that are all explicit func-
tionals of the charge density, therefore avoiding the necessity of solving the
single-particle Schr
¨
dinger equations for the fictitious particles and using the
Kohn-Sham orbitals. Such a simplification allows the method to scale linearly
with the system size, and, therefore, makes it capable of handling significantly
more atoms than standard DFT. The memory requirements are also signifi-
cantly reduced. However, the approximations introduced in describing the
kinetic energy make the method less transferable than standard DFT. Lastly,
OFDFT is particularly well suited for hybrid calculations because having the
energy as a function of only the electronic density makes it easer to evaluate
the coupling term between the quantum and the classical regions than it is
when using standard DFT. Other hybrid methodologies that take advantage
of OFDFT when coupling classical and quantum regions are, for instance,
those of Wesolowski and Warshel
247
and of Kl ¨ ner et al.
248
In the method
of Choly and co-workers, the system is divided into two parts: a small OFDFT
region, where the electronic behavior is important, and a much larger region
