  Preparation of solid solutions represents an effective means to improve the
photocatalytic properties of semiconductor-based materials. Nevertheless, the
effects of site-occupancy disorder on the mixing stability and electronic
properties of the resulting compounds are difficult to predict and consequently
many experimental trials may be required before achieving enhanced
photocatalytic activity. Here, we employ first-principles methods based on
density functional theory to estimate the mixing free energy and the structural
and electronic properties of (GaP)$_{x}$(ZnS)$_{1-x}$ solid solutions, a
representative semiconductor-based optoelectronic material. Our method relies
on a multi-configurational supercell approach that takes into account the
configurational and vibrational contributions to the free energy. Phase
competition among the zinc-blende and wurtzite polymorphs is also considered.
We demonstrate overall excellent agreement with the available experimental
data: (1)~zinc-blende emerges as the energetically most favorable phase,
(2)~the solid solution energy band gap lies within the $2$--$3$~eV range for
all compositions, and (3)~the energy band gap of the solid solution is direct
for compositions $x \le 75$\%. We find that at ambient conditions most
(GaP)$_{x}$(ZnS)$_{1-x}$ solid solutions are slightly unstable against
decomposition into GaP- and ZnS-rich regions. Nevertheless, compositions $x
\approx 25$, 50, and 75\% render robust metastable states that owing to their
favorable energy band gaps and band levels relative to vacuum are promising
hydrogen evolution photocatalysts for water splitting under visible light. The
employed theoretical approach provides valuable insights into the
physicochemical properties of potential solid-solution photocatalysts and
offers useful guides for their experimental realization.
