Chemistry Reference
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of
T
h
3
. The corrections are then computed on the electronic mesh,
T
h
3
.The
variational problem is then solved using conjugate gradients. More details on
the method can be found in the original paper.
253
The OFDFT-QC method
was demonstrated by studying one and two vacancies in large Al crystals.
First-Principles Green's Function Boundary Condition Method
The first-principles Green's function boundary condition (FP-GFBC)
method introduced by Woodward et al. in 2001
254-256
is a generalization of
the flexible boundary condition method (GFBC), discussed earlier. As before,
the methodology is directed to the study of dislocation properties, with parti-
cular attention to core structures. As in the earlier GFBC work, the dislocation
core is embedded into a medium where the lattice Green's function is used to
compute a stress field consistent with the response function of the bulk mate-
rial. We refer to the earlier description of the general principles of the Green's
function boundary condition approach. The main difference between the two
methodologies is that in the first-principles version, the core structure (region 1
in Figure 6) is modeled using an ab initio (DFT) approach instead of a classical
one. Pseudopotential plane-wave methods are a particularly good choice for
such a modeling because they allow for an easy calculation of the
Hellmann-Feynman forces that are used to relax the core domain. It is impor-
tant to remark that the possibility of using DFT, instead of an empirical poten-
tial, comes from the ability of the method to use minimal computational cell
sizes without incurring significant incompatibility forces.
From a computational point of view, the use of the DFT method
employed by the authors
257-261
required the use of 3D periodic boundary con-
ditions. However, the problem under examination, the determination of the
equilibrium core structure of an isolated dislocation, only allows periodicity
along the direction of the dislocation line. Therefore, the authors proposed
two possible simulation cells to circumvent such an impasse: One where the
standard cell used in GFBC is embedded within a vacuum region that isolates
it from its periodic images (Figure 15(a)], and one where a much larger region
3 is considered, instead of the vacuum [Figure 15(b)].
The authors found that the two geometries lead to quantitatively identi-
cal results, as long as the thickness of region 3 is large enough to screen out
the charge dipole that forms at the outer cell boundary. However, the geome-
try of Figure 15(b) is significantly more efficient from a computational point of
view.
Applications
The FP-GFBC has been used to model dislocation core
structure in Mo and Ta.
254-256
Quantum Atomistic Static Interface Method
The quantum atomistic static interface (QuASI) methodology of Tavazza
et al.
262-264
is inspired by the flexible boundary condition idea (e.g., the
