45
not have information about the stability of the materials in aqueous conditions
which is also explored in this work for the stability of the photocatalysts
under in-situ conditions.
In chapter 1 a few different methods to calculate the bandgap of the semiconductors
were discussed along with their pros and cons. It has also been
pointed out that the calculation of the bandgap in a screening study should be
reasonably accurate and at the same time efficient. The previously discussed
GLLB-SC functional meets both the criteria in most of the cases. Therefore, in
the present study the bandgap of 2400 compounds has been calculated with
the GLLB-SC functional. Additionally, to test the validity of the calculated
bandgap with the GLLB-SC functional the previously discussed hybrid functional
HSE06 and the many body perturbation theory in different flavors like
G0W0, GW0 and GW have also been used for a few selected materials. The
comparison is shown in the Figure 5.2. The plot is divided into the high and
low bandgap materials. The figure shows that HSE06 tends to underestimate
the bandgap a bit with respect to GLLB-SC. On the other hand, GW which
is an eigenvalue self-consistent flavor of the GW approximation dovetails very
well with the GLLB-SC bandgaps in the low bandgap region. Additionally,
GLLB-SC has a mean absolute error (MAE) of 0.38 eV with respect to GW
thus closer to the GW predictions as compared to HSE06 and G0W0 which
have the MAE of 0.46 and 0.51 eV respectively. GW0, being closest to the GW
prediction with a MAE of only 0.29 eV, is highly computationally expensive as
compared to GLLB-SC. Therefore, GLLB-SC being reasonably accurate and
an order of magnitude computationally cheaper than the GW approximation
serves the purpose of bandgap prediction in a screening study. Table 5.1 summarizes
the above mentioned mean absolute (signed) error in the bandgap of
the compounds lying in the low region calculated with different methods with
respect to the other methods.
Table 5.1: Mean absolute (signed) error in eV for the materials in the small
bandgap region in Figure 5.2 using LDA, GLLB-SC, HSE06, G0W0 and GW0
and GW
xcref LDA GLLB-SC HSE06 G0W0 GW0 GW
xc
LDA - 1.64 (-1.64) 1.21 (-1.21) 1.08 (-1.08) 1.30 (-1.30) 1.59 (-1.59)
GLLB-SC 1.64 (1.64) - 0.61 (0.43) 0.59 (0.56) 0.52 (0.34) 0.38 (0.05)
HSE06 1.21 (1.21) 0.61 (-0.43) - 0.25 (0.13) 0.29 (-0.09) 0.46 (-0.38)
G0W0 1.08 (1.08) 0.59 (-0.56) 0.25 (-0.13) - 0.22 (-0.22) 0.51 (-0.51)
GW0 1.30 (1.30) 0.52 (-0.32) 0.29 (0.09) 0.22 (0.22) - 0.29 (-0.29)
GW 1.59 (1.59) 0.38 (-0.05) 0.46 (0.38) 0.51 (0.51) 0.29 (0.29) -