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underestimates with respect to HSE06). The GW 0 approximation
gives a MAE of around 0.5 eV for the GLLB-SC and slightly
less than 0.3 eV for HSE06 and the other two GW levels. The
GLLB-SC is the closest to the self-consistent GW with a MAE of
0.38 eV when compared with HSE06 and G 0 W 0 which have a
MAE close to 0.5 eV.
GLLB-SC has a mean relative errors (MRE) with respect to
GW equal to 15% better that the MRE for HSE06 and G 0 W 0
(16 and 18%, respectively), while GW 0 performs better with an
error of 10%. The HSE06 error increases to 23% for the wide
bandgap set, as shown in the Supporting Information.
The computational costs required for the methods are very
different. G 0 W 0 is one or two orders of magnitude more expensive
that GLLB-SC which is slightly more expensive than a
standard GGA calculation. HSE06 is slightly more expensive
than GLLB-SC but still cheaper than G 0 W 0 . The computational
cost increases even further for the (partial) self-consistent GW
where more iterations are needed.
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The bandgaps calculated with GLLB-SC can now be used as
a descriptor in a screening study. In the following section, we
propose a handful of materials that can be used in a water splitting
device using a high-throughput screening approach.
3. Screening for Water Splitting Materials
The starting point of a screening study is to defi ne the descriptors
that correlate the microscopic quantities calculated using
ab-initio quantum mechanics simulations with the macroscopic
properties of a material. 40 For example, the formation enthalpy
of a compound can describe its stability, the bandgap its absorption
properties, and so on.
The set of data calculated here can provide the search space
for the computational screening of materials for different
applications, such as light absorbers (photovoltaics and photocatalysis),
transparent conductors, and thermoelectrics. Here,
we illustrate this approach by proposing a handful of materials
that can be used to produce energy through photoelectrochemical
splitting of water into oxygen and hydrogen using
solar light. In a water splitting device, solar energy is used to
divide water into hydrogen and oxygen: the solar light is harvested
by a semiconductor and electron-hole pairs are created.
The electrons and holes then reach the surface of the semiconductor
where, if they are at the right potentials with respect
to the redox levels of water, the electrons reduce the protons
and the holes oxidize the water. The properties required by a
semiconductor to be used in this device are: i) stability, ii) high
light absorption, iii) photogenerated charges with appropriate
energies. In addition iv) good electron-hole mobility, v) high
catalytic activity, vi) non-toxicity, and vii) cost-effectiveness are
desirable properties. The screening is based on three criteria:
stability, bandgap in the visible light range, and band edges of
the semiconductor well positioned versus the redox levels of
water. These represent the descriptors for the properties (i–iii),
i.e., a stable material with a well positioned bandgap in the visible
light range. A more detailed explanation of the water splitting
device can be found in previous works. 7,8
Previous studies have described the search for new compounds
to be used in a water splitting cell both in the perovskite
crystal symmetry (cubic, 7,8 double, 41 and layered in the Ruddlesden
Popper phase 25 ) and in the oxynitride and nitride class
of materials using a data mining approach. 42 Here, instead of
searching for completely new materials, we consider structures
1400915 (4 of 7) wileyonlinelibrary.com © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
Adv. Energy Mater. 2015, 5, 1400915
www.advenergymat.de
Table 1. Mean absolute (signed) error, in eV, for the small bandgaps of the materials in Figure 2 calculated using LDA, GLLB-SC, HSE06, G 0 W 0 , GW 0
and GW.
xc ref LDA GLLB-SC HSE06 G 0 W 0 GW 0 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)
G 0 W 0 1.08 (1.08) 0.59 (−0.56) 0.25 (−0.13) – 0.22 (−0.22) 0.51 (−0.51)
GW 0 1.30 (1.30) 0.52 (−0.34) 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) –
Figure 3. a) HSE06, b) G 0 W 0 , c) GW 0 , and d) GW bandgaps as a function
of the GLLB-SC gaps. All the methods except GW underestimate the
gaps with respect to the GLLB-SC. The signed error of GLLB-SC and GW
is 0.05 eV.