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The energy differences between the face-centered cubic (FCC) and hexagonalclosed packed (HCP) structures of the argon (Ar) crystal are studied using thefirst-principles electronic-structure approach at the level of random phaseapproximation (RPA) plus renormalized single exitation (rSE) correction. Bytreating both structures at equal footing (i.e., employing the samecomputational supercell and k grid sampling), our RPA+rSE calculations showthat, at zero temperature, the FCC structure is lower in energy than the HCPstructure 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 indetermining the relative stability of the two structures, whereas the electroncorrelation effect dominates. We further examine the equation of states in thehigh pressure regime, and our RPA+rSE results, complemented with phononcontributions, show excellent agreement with available experimental data.Finally, by computing the Gibbs free energies for both the FCC and HCP atdifferent temperatures, we are able to generate a $T$-$P$ phase diagram for theAr crystal, disclosing the pressure-temperature range for each phase. Ourcalculations show that the FCC phase has a slightly larger entropy and volumethan HCP phase at the temperature and pressure condition.

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