  We calculate superconducting transition temperatures ($T_{\rm c}$) in sulfur
hydrides H$_{2}$S and H$_{3}$S from first principles using the density
functional theory for superconductors. At pressures of $\lesssim$150 GPa, the
high values of $T_{\rm c}$ ($\gtrsim$130 K) observed in the recent experiment
[A. P. Drozdov, M. I. Eremets, and I. A. Troyan, arXiv:1412.0460] are
accurately reproduced by assuming that H$_{2}$S decomposes into $R3m$-H$_{3}$S
and S. For the higher pressures, the calculated $T_{\rm c}$s for
$Im3m$-H$_{3}$S are systematically higher than those for $R3m$-H$_{3}$S and the
experimentally observed maximum value (190 K), which suggests the possibility
of another higher-$T_{\rm c}$ phase. We also quantify the isotope effect from
first principles and demonstrate that the isotope effect coefficient can be
larger than the conventional value (0.5) when multiple structural phases
energetically compete.
