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already optimized by nature, i.e., known to exist. While no new
compounds will be proposed, this scheme has the advantage of
the known synthesis procedure so that testing and validation
can be prioritized.
Although all the materials studied here are experimentally
known, i.e., they are stable, or at least metastable, little is
known about their stability in contact with water. The corrosion
problem can be investigated using the so-called Pourbaix
diagrams, where solid and dissolved substances are combined
in a single phase diagram so that the stable species (solid and/
or aqueous ion) can be determined, as a function of pH and
potential. The total energies of the solid phases, taken from the
ICSD and the Materials Project databases, 9,12 are obtained with
DFT (using the RPBE xc-functional 43 ). Data for the dissolved
ions, instead, come from experiments. 44,45 This method for
evaluating stability in water has been already investigated and
validated elsewhere. 33,46
It is diffi cult to defi ne a single energy threshold under which
a material is considered stable because of metastability, reaction
kinetics, effect and passivation of the surfaces as well as
inaccuracy in the calculations and experiments. Here, we consider
a generous energy threshold of 1 eV/atom. We propose
25 compounds ( Figure 4 ), that also fulfi ll the criteria relating
to the bandgap and band edges positions, stable in a potential
window corresponding to the working potential of the device
(bare redox levels of water plus reaction overpotentials and
quasi-Fermi levels, i.e., between −0.4 and 2.2 V) and in neutral
pH (pH = 7). Neutral pH is desirable because it is not harmful
to environment and not corrosive however the effi ciency of the
device can be improved by operating at very acid or alkaline
conditions.
The bandgaps have been calculated with the GLLB-SC functional.
The bare energy required to split water is 1.23 eV. This
energy is not enough to run the water splitting reactions and
some overpotentials are needed (0.1 eV for hydrogen evolution
and 0.4 eV for oxygen production 47 ). When the semiconductor
is under illumination and electron-hole pairs are created, the
electron and hole densities are above their equilibrium values
and a single Fermi level cannot describe their populations.
The quasi-Fermi levels describe these non-equilibrium populations,
located ≈0.25 eV below (above) the conduction (valence)
bands for an undoped semiconductor and they correspond to
the effective energy of the photogenerated electrons and holes.
The minimum bandgap to run the water splitting reaction is at
least 2 eV. The maximum realistic effi ciency of a water splitting
device is around 7%. 48 This effi ciency is quite low, especially
when compared with the standard technologies for photovoltaics.
A higher effi ciency can be obtained using a multiphoton
device 7,49 albeit increasing the technological diffi culties and
thus the price of the device. In this work, we focus on the onephoton
device emphasizing the simplicity of the device rather
than effi ciency. 50
There are several methods to obtain the positions of the
band edges, 51,52 all computationally rather demanding and not
suited to be used in a screening study. Here, the positions of
the band edges have been calculated using an empirical equation
based on the geometrical average of the electronegativities
in the Mulliken scale of the individual atoms that form the
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Adv. Energy Mater. 2015, 5, 1400915
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Figure 4. The most stable materials with potential for one-photon water splitting. The stability in water of each material is calculated as the energy
difference between the material and the most stable phases (solid and aqueous) in which it can separate in a potential range between −0.4 and 2.2 V
and at pH = 7. The color scale runs from green (i.e., stable) to red (unstable compounds). In the plot, the indirect and direct positions of the valence
and conduction band edges (BE) are indicated in black and red as well as the indirect and direct bandgap (BG).