Structural and Electronic properties of $\beta$-In$_{2}$X$_{3}$ (X = O, S, Se, Te) using \emph{ab initio} calculations*

Several III-VI body-centered tetragonal layered compounds belonging to space group I4$_{1}$/\emph{amd} have been a subject of interest recently because of their potential applications in high efficiency and environmentally friendly copper-indium-gallium-selenide (CIGS) solar cells and molecules. Here we have studied the structural, energetic, and electronic properties of four compounds $\beta$-In$_{2}$X$_{3}$ (X = O, S, Se, Te), in this space group. Using first principles computations, we have fully determined the lattice constants \emph{a} and \emph{c}, as well as 10 internal parameters that define this unique structure of primitive unit cells of 40 atoms. For $\beta$-In$_{2}$S$_{3}$ our computed values are found to be consistent with experimental measurements. The bulk modulus B, local electronic density of states (LDOS), total density of states (DOS), and band gap E$_{f}$ of these phases have been investigated.