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Screened-exchange density functional theory description of the electronic structure and phase stability of the chalcopyrite materials AgInSe$_2$ and AuInSe$_2$

We present a systematic assessment of the structural properties, the electronic density of states, the charge densities, and the phase stabilities of AgInSe$_2$ and AuInSe$_2$ using screened exchange hybrid density functional theory, and compare their properties to those of CuInSe$_2$. For AgInSe$_2$, hybrid density functional theory properly captures several experimentally measured properties, including the increase in the band gap and the change in the direction of the lattice distortion parameter $u$ in comparison to CuInSe$_2$. While the electronic properties of AuInSe$_2$ have not yet been experimentally characterized, we predict it to be a small gap ($\approx 0.15$ eV) semiconductor. We also present the phase stability of AgInSe$_2$ and AuInSe$_2$ according to screened-exchange density functional theory, and compare the results to predictions from conventional density functional theory, results tabulated from several online materials data repositories, and experiment (when available). In comparison to conventional density functional theory, the hybrid functional predicts phase stabilities of AgInSe$_2$ in better agreement with experiment: discrepancies in the calculated formation enthalpies are reduced by approximately a factor of three, from $\approx$ 0.20 eV/atom to $\approx$ 0.07 eV/atom, similar to the improvement observed for CuInSe$_2$. We further predict that AuInSe$_2$ is not a stable phase, and can only be present under non-equilibrium conditions.