Crystal structures and superconductivity of carbonaceous sulfur hydrides at pressures up to 300 GPa

To explore the crystal structure of the recently claimed room-temperature superconducting carbonaceous sulfur hydrides, we searched for $\ensuremath{\approx}250\phantom{\rule{0.16em}{0ex}}000$ structures over $\ensuremath{\approx}800$ stoichiometries at 300 GPa via advanced crystal structure searching and cluster expansion method. Only several metastable high-temperature superconductors were identified, whose structures can be classified into hydrogen-rich molecular crystals and low-level carbon-doped ${\mathrm{H}}_{3}\mathrm{S}$-like structures by constructing the ternary phase diagram and simulating the electron-phonon interactions. The C--S--H molecular crystals are composed of ${\mathrm{CH}}_{4}, {\mathrm{SH}}_{6}$, and ${\mathrm{H}}_{2}$ molecules, where the superconductivity (with the highest superconducting critical temperature ${T}_{c}$ is 156 K found in ${\mathrm{CSH}}_{48}$ at 300 GPa) is mainly contributed to by ${\mathrm{H}}_{2}$ units, implying their ${T}_{c}$ values are unlikely to be higher than that of metallic molecular hydrogen (${T}_{c}$ of 242 K at 450 GPa). The highest ${T}_{c}$ of low-level carbon-doped C--S--H compounds (up to 64 atoms in the primitive cell) at 300 GPa was estimated as 189 K for ${\mathrm{H}}_{3}{\mathrm{S}}_{0.917}{\mathrm{C}}_{0.083}$. Our results provide a comprehensive map between the crystal structure and superconductivity of carbonaceous sulfur hydride materials at high pressures.