for ternary/tertiary compounds only if their chemical environment does not
differ significantly from the compounds used in the fitting procedure. Hence,
a test set containing a mix of binary and ternary compounds has been selected
for the validation of the fitting.
Table 3.3 and 3.4 show the heats of formation of the test set without and
with the fitting respectively. The clear decrease in the MAE and shows the
absence of overfitting. As expected in any regression scheme, the improvement
with the fitted model is not as much as the improvement seen in the training
In the test set also, the mBEEF predictions without the fitting has the
same quality as the other functionals with the fitting and the improvement
with the fitting is only moderate in the case of the mBEEF. Therefore, a
reasonable prediction with the mBEEF can be obtained even without using
the fitting with only negligibly increased computational cost as compared to
The rapidly growing area of the computational screening of the energy materials
requiring reasonable predictions of the stability has led forward this work.
The synergetic use of the DFT total energies and the experimental heats of
formation provides a framework to improve the predictions. Originally, the
scheme was developed for the PBE+U functionals but in this work similar
improvements has been seen for the other functionals like PBE, RPBE, TPSS
and mBEEF as well.
We see that the recently developed mBEEF functional which has been
optimized using variety of experimental dataset gives better predictions as
compared to the other functionals. Additionally, the mBEEF functional also
provides reasonable estimate of the uncertainties in the predictions, the feature
which other functionals used in this work lack. However, the uncertainties
estimated by the mBEEF ensemble is in general overestimated which can further
be reduced by using the FERE scheme along with the reduction of the
true error as well.
Despite giving improved results FERE scheme has some drawbacks as well.
The corrections are primarily based on nature of the bonding environment in
the training set, therefore, it may not significantly improve the predictions for
the systems differing from the systems used in the training set, for example, in
metal alloys which have significantly different chemical environment than the
semiconductors used in the training set. Therefore, higher level functionals