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We calculate superconducting transition temperatures ($T_{\rm c}$) in sulfurhydrides H$_{2}$S and H$_{3}$S from first principles using the densityfunctional theory for superconductors. At pressures of $\lesssim$150 GPa, thehigh values of $T_{\rm c}$ ($\gtrsim$130 K) observed in the recent experiment[A. P. Drozdov, M. I. Eremets, and I. A. Troyan, arXiv:1412.0460] areaccurately reproduced by assuming that H$_{2}$S decomposes into $R3m$-H$_{3}$Sand 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 theexperimentally observed maximum value (190 K), which suggests the possibilityof another higher-$T_{\rm c}$ phase. We also quantify the isotope effect fromfirst principles and demonstrate that the isotope effect coefficient can belarger than the conventional value (0.5) when multiple structural phasesenergetically compete.

First-principles study of the pressure and crystal-structure dependences of the superconducting transition temperature in compressed sulfur hydrides