  Silver-based chalcohalide anti-perovskites (CAP), Ag$_{3}$BC (B = S, Se; C =
Cl, Br, I), represent an emerging family of energy materials with intriguing
optoelectronic, vibrational and ionic transport properties. However, the
structural features and phase stability of CAP remain poorly investigated to
date, hindering their fundamental understanding and potential integration into
technological applications. Here we employ theoretical first-principles methods
based on density functional theory to fill this knowledge gap. Through crystal
structure prediction techniques, ab initio molecular dynamics simulations, and
quasi-harmonic free energy calculations, we unveil a series of previously
overlooked energetically competitive phases and temperature-induced phase
transitions for all CAP. Specifically, we identify a new cubic $P2_{1}3$
structure as the stable phase of all CAP containing S both at zero temperature
and $T \neq 0$ K conditions. Consequently, our calculations suggest that the
cubic $Pm\overline{3}m$ phase identified in room-temperature X-ray diffraction
experiments is likely to be metastable. Furthermore, for CAP containing Se, we
propose different orthorhombic ($Pca2_{1}$ and $P2_{1}2_{1}2_{1}$) and cubic
($I2_{1}3$) structures as the ground-state phases and reveal several phase
transformations induced by temperature. This theoretical investigation not only
identifies new candidate ground-state phases and solid-solid phase
transformations for all CAP but also provides insights into potential stability
issues affecting these highly anharmonic superionic materials.
