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We report a comparative theoretical study of the \textit{Pnma} and\textit{R-3m} phases of Sb$_2$S$_3$, Bi$_2$S$_3$, and Sb$_2$Se$_3$ close toambient pressure.  Our enthalpy calculations at 0 K show that at ambient pressure the\textit{R-3m} (tetradymite-like) phase of Sb$_2$Se$_3$ is energetically morestable than the \textit{Pnma} phase, contrary to what is observed forSb$_2$S$_3$ and Bi$_2$S$_3$, and irrespective of the exchange-correlationfunctional employed in the calculations.  The result for Sb$_2$Se$_3$ is in contradiction to experiments where allthree compounds are usually grown in the \textit{Pnma} phase.  This result is further confirmed by free-energy calculations taking intoaccount the temperature dependence of the unit-cell volumes and phononfrequencies.  Lattice dynamics and elastic tensor calculations further show that both\textit{Pnma} and \textit{R-3m} phases of Sb$_2$Se$_3$ are dynamically andmechanically stable at zero applied pressure.  Since these results suggest that the formation of the \textit{R-3m} phase forSb$_2$Se$_3$ should be feasible at close to ambient conditions, we provide atheoretical crystal structure and simulated Raman and infrared spectra to helpin its identification. We also discuss the results of the two published worksthat have claimed to have synthesized tetradymite-like Sb$_2$Se$_3$.  Finally, the stability of the \textit{R-3m} phase across the three group-15\textit{A$_2$X$_3$} sesquichalcogenides is analysed based on their van derWaals gap and X-X in-plane geometry.

Theoretical study of the stability of the tetradymite-like phases of Sb$_2$S$_3$, Bi$_2$S$_3$, and Sb$_2$Se$_3$