Chemistry Reference
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because, as the authors note, the classical energy can be viewed as an approx-
imation of the DFT energy functional that has been minimized with respect to
the charge density. This means that this approach contains more approxima-
tions than the one where OFDFT is used to evaluate the hand-shake energy,
but, also, that it is much lighter computationally. The final expression for the
total energy is obtained by substituting Eq. [60] into Eq. [59]:
E
½
I
þ
II
¼
E
cl
½
I
þ
II
E
cl
½
I
þ
E
DFT
½
I
;
½
61
where, according to the Hohenberg-Kohn theorem,
E
DFT
is found, within
the Born-Oppenheimer approximation, by minimizing a functional of the
charge density
½
I
min
I
r
I
;
R
I
E
DFT
½
I
¼
E
DFT
½
r
½
62
where
R
I
are the ion coordinates in region I. For a detailed discussion of how
such a scheme affects the calculation of the forces, we refer to the original
paper.
241
The second coupling schemes computes
E
hand shake
using OFDFT.
The use of an orbital-free approach, instead of a standard DFT, is particularly
effective in this step because the only information available on region II is its
approximate charge density
½
I
;
II
r
II
and the positions of the atoms in
R
II
, and, as
discussed above, that is all OFDFT needs to determine the energy. In this
scheme, the interaction energy is given by
E
hand shake
½
I
;
II
¼
E
OF
½
I
þ
II
E
OF
½
I
E
OF
½
II
½
63
where the computational advantage of using this approach versus simulating
the whole system with OFDFT comes from the cancellation hidden in
E
OF
½
I
þ
II
E
OF
½
I
, when Eq. [63] is inserted in Eq. [59], and from the fact
that
E
OF
½
I
þ
II
is found by minimizing the OFDFT energy functional with
respect to
r
I
being the charge density in region I). For details on
how the method can be implemented, we refer to the original paper.
241
r
I
only (
DFT/OFDFT and Quasi-continuum (OFDFT-QC, QCDFT)
In the previous section, we discussed a hybrid methodology that couples
orbital-free DFT (OFDFT) to classical potentials. A basic description of the
OFDFT was also given. Another possibility is to couple OFDFT to quasicon-
tinuum methods. Such an approach has been suggested by Fago et al. in
2004
249-251
and followed by Gavini et al.
252
in 2007. OFDFT lends itself
very easily to coupling with QC methods because it is significantly faster
than traditional Kohn-Sham DFT, and speed is crucial when millions of
DFT calculations are needed during a typical hybrid simulation.
