Crystal Structure Prediction and 0 K Stability Assessment of Hypothetical Re₃Zr Polymorphs: Vibrational, Elastic, and...

Re₃Zr has recently been proposed in the cubic Pm-3n structure. Its alternative atomic arrangements and thermodynamic position within the Re-Zr system have not been systematically resolved. In this work, CALYPSO particle-swarm structure searches combined with density functional theory identify five Re₃Zr polymorphs with Cmcm, Fmmm, Immm, P4/mmm, and Fm-3m symmetries and compare them consistently with the reported Pm-3n phase. Formation enthalpies, a selected-phase partial convex hull, phonon dispersions, elastic properties, sound velocities, elastic Debye temperatures, electronic structures, and bonding characteristics are evaluated. All five CALYPSO structures lie below Pm-3n in fixed-composition energy, with Cmcm being the lowest. The Cmcm phase has a formation enthalpy of -0.257 eV atom^-1 and lies approximately 0.042 eV atom^-1 above the selected-phase partial hull, identifying it as a low-lying off-hull metastable candidate at 0 K. AIMD simulations at 300 and 1000 K show no obvious structural reconstruction of the Cmcm framework over the simulated time scales. All six structures exhibit no imaginary phonon frequencies and satisfy the corresponding mechanical-stability criteria. Their elastic responses are strongly structure dependent: P4/mmm has the largest Chen-Tian hardness estimates and elastic Debye temperature, whereas Fm-3m shows the weakest elastic anisotropy. All six polymorphs are metallic, with Fermi-level states dominated by Re-5d orbitals and predominantly delocalized bonding. These results provide a thermodynamically constrained 0 K reference for future synthesis, phase identification, and finite-temperature or kinetic investigations of hypothetical Re₃Zr polymorphs.