Chemistry Reference
In-Depth Information
The philosophy behind the transparent interface method is to optimize the
description of the interatomic forces across the interface, instead of focusing on
the accurate reproduction of the total energy of the system. The method utilizes
a single energy functional to describe the whole system and pseudoatoms
to connect the quantum and classical regions. More in detail, a pseudoatom
is placed in between each quantum-described oxygen and classically described
silicon to correctly terminate the quantumwave functions, and the Hamiltonian
for the whole system is given by
X
X
2
2
m
IQ
þ
j
P
IQ
j
Z
IQ
Z
JQ
j
R
IQ
;
R
m
g;
r
½
r
;
r
Þ
H
¼
j
þ
E
elec
ðf
R
IQ
R
JQ
IQ
IQ
>
JQ
½
71
X
2
2
m
IC
þ
j
P
IC
j
þ
U
ðf
R
IC
gÞ þ
U
ðf
R
IQ
;
R
IC
gÞ
IC
where IQ and IC describe particles in the quantum and classical regions,
respectively,
R
m
and
r
are the nuclear and electronic coordinates for the pseu-
doatoms, and
m
is the index of the pseudoatom.
E
elec
¼
E
ee
is the
total ground-state electronic energy, i.e., the sum of the electron kinetic
energy, the electron-ion interaction and the electron-electron interaction.
The first three terms in Eq. [71] describe the quantum region in the presence
of pseudoatoms, while the fourth and fifth terms define the kinetic and poten-
tial energy of the classical part of the system. The last term contains the sum of
all the interactions between quantum and classical ions.
The pseudoatoms are introduced to terminate the wave functions of the
quantum cluster in such a way that the structure and forces on the quantum
cluster are as close as possible to those of the same subsystem within an all-
quantum system. The pseudoatoms are therefore placed along a straight line
between the quantum oxygen and the classical silicon, at a fixed distance from
the oxygen [
d
T
e
þ
E
eI
þ
82
a
0
(Bohr)]. Also, they do not carry any kinetic energy, so
as not to exert any direct influence on the dynamics of the system. Lastly, to
obtain an interface as smooth as possible, the same classical potential is used
for modeling both the interactions between classical and quantum ions and the
interactions between classical and classical ions.
In the transparent interface method, the forces on each atom are derived
from the gradient of the total potential energy in Eq. [71]. However, the con-
straint forces acting on quantum atoms at the boundary, due to the constaints
imposed on the pseudoatoms, are neglected in this approach, leading to an
approximation of the Hamiltonian equations that provides correct forces
and dynamics (within the limit of a classical force field) but violates energy
conservation.
More details on the explicit calculation of the forces and the implemen-
tation of the BO-DFT-MD method within a generalized gradient approxima-
tion (GGA)
285
can be found in the original papers.
281-283
¼
1
:
