Chemistry Reference
In-Depth Information
energies was 0.48 eV, while the mean deviation was
2
0.46 eV, indicating that
this functional overbinds CO in almost all cases. Similar calculations with the
RPBE GGA functional gave a mean deviation of
2
0.12 eV and a mean absol-
ute deviation of 0.25 eV. Abild-Pedersen and Andersson also tested a simple
correction for the adsorption energy of CO that involves examining molecular
orbital properties of CO as calculated with the DFT functional being used.
Applying this correction to the RPBE GGA results gave a mean deviation
in the overall CO adsorption energy of 0.06 eV. This is an encouraging
sign that the systematic errors associated with using GGA functionals to pre-
dict molecular adsorption energies can be reduced, but this method is not yet
well developed for
the general problem of understanding molecular
adsorption.
One general explanation for the systematic inaccuracies of DFT for adsorp-
tion energies is that these calculations inherently involve comparing chemi-
cally dissimilar states, namely an isolated molecule and a molecule
chemically bound to a surface. An even simpler example of this situation is
to consider the bond strength of simple molecules. As a specific example,
Fuchs et al. (as part of a larger study) examined the bond energy of N
2
as
predicted by various DFT functionals.
14
They found that the LDA functional
overbinds N
2
by about 1 eV
/
atom. This overbinding is reduced to 0.5 and 0.2
eV
atom by using the PBE and RPBE GGA functionals, respectively. The
imprecision in predicted bond energies is not a feature that appears only in
plane-wave DFT calculations, as the information for molecular energies
from localized basis set DFT calculations in Table 10.1 indicates.
The overprediction of binding energies for simple molecules can have con-
sequences for
ab initio
thermodynamic calculations involving these species.
In Chapter 7 we examined the stability of bulk oxide materials using this
approach. In order to quantitatively predict the conditions at which bulk
phases were in equilibrium, the chemical potential of O
2
had to be calculated
using Eq. (7.6), which includes a contribution from the total energy of O
2
. One
way to correct for the imprecision of DFT for total energies of this kind is to
use experimental data when it is available. When this approach is used, it is
important that it is clearly stated.
/
10.4 DFT
1
X METHODS FOR IMPROVED TREATMENT
OF ELECTRON CORRELATION
The discussion of the hierarchy of functionals in Section 10.2 highlighted the
observation that while the exchange energy of a collection of electrons can, in
principle, be evaluated exactly, the correlation energy cannot. As a result,
it is reasonable to be particularly concerned about the reliability of DFT
