  Binary tin sulfides are appealing because of their simple stoichiometry and
semiconducting properties and are potentially cost-effective optoelectronic
materials. The multivalency of Sn allows yet more intermediate compositions,
Sn$_x$S$_y$, whose structures and properties are of interest.Sn$_2$S$_3$ is
already under consideration as a mixed-valence semiconductor. Other
intermediate compositions have remained elusive. Here we report a comprehensive
study of phase stability of the Sn$_x$S$_y$ series compounds, utilizing
swarm-intelligence crystal structure search method combined with
first-principles energetic calculations. We find that the stability of
mixed-valence Sn$_x$S$_y$ compounds with respect to decomposition into
pure-valence SnS and SnS$_2$ is in general weaker than the Sn$_x$O$_y$
counterparts, likely due to differences in chemical bonding. Besides
identifying the experimentally discovered stable phases of Sn$_2$S$_3$, our
calculations indicate that the Sn$_3$S$_4$ phase is another mixed-valence
composition which shows marginal stability with respect to decomposition into
SnS and SnS$_2$. Other studied compositions may be metastable under ambient
conditions, with slightly positive formation enthalpies. We find two structures
of Sn$_3$S$_4$ having comparably low energies, both of which feature
one-dimensional chain-like fragments obtained by breaking up the edge-connected
octahedral layers of SnS$_2$. Both structures indicate lattice phonon stability
and one shows quasi-direct band gap with a calculated value of 1.43 eV, ideal
for solar absorbers. A further analysis of the composition-structure-property
relationship supports the notion that lowdimensional Sn-S motifs and van der
Waals interaction may lead to diverse structure types and chemical
compositions, having functional properties that are yet to be identified in the
Sn$_x$S$_y$ series with mixed valency.
