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Phase Stability of the Argon Crystal: A First-Principles Study Based on Random Phase Approximation plus Renormalized Single Excitation Corrections

The energy differences between the face-centered cubic (FCC) and hexagonal closed packed (HCP) structures of the argon (Ar) crystal are studied using the first-principles electronic-structure approach at the level of random phase approximation (RPA) plus renormalized single exitation (rSE) correction. By treating both structures at equal footing (i.e., employing the same computational supercell and k grid sampling), our RPA+rSE calculations show that, at zero temperature, the FCC structure is lower in energy than the HCP structure over a wide pressure range. The influence of zero-point energy (ZPE) is also studied and and it is found that ZPE only plays a secondary role in determining the relative stability of the two structures, whereas the electron correlation effect dominates. We further examine the equation of states in the high pressure regime, and our RPA+rSE results, complemented with phonon contributions, show excellent agreement with available experimental data. Finally, by computing the Gibbs free energies for both the FCC and HCP at different temperatures, we are able to generate a $T$-$P$ phase diagram for the Ar crystal, disclosing the pressure-temperature range for each phase. Our calculations show that the FCC phase has a slightly larger entropy and volume than HCP phase at the temperature and pressure condition.