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We computed the optical properties and the folded and unfolded band structure of Cu-doped KCl crystals. The calculations use the plane-wave pseudo-potential approach implemented in the ABINIT electronic structure package within the first-principles density-functional theory framework. Cu substitution into pristine KCl crystals requires calculation by the supercell (SC) method from a theoretical perspective. This procedure shrinks the Brillouin zone, resulting in a folded band structure that is difficult to interpret. To solve this problem and gain insight into the effect of cuprous ion (Cu+) on electronic properties; We unfolded the band structure of SC KCl:Cu to directly compare with the band structure of the primitive cell (PC) of pristine KCl. To understand the effect of Cu substitution on optical absorption, we calculated the imaginary part of the dielectric function of KCl:Cu through a sum-over-states formalism and broke it down into different band contributions by partially making an iterated cumulative sum (ICS) of selected valence and conduction bands. As a result, we identified those interband transitions that give rise to the absorption peaks due to the Cu ion. These transitions include valence and conduction bands formed by the Cu-3d and Cu-4s electronic states. To investigate the effects of doping position, we consider different doping positions, where the Cu dopant occupies all the substitutional sites replacing host K cations. Our results indicate that the doping position's effects give rise to two octahedral shapes in the geometric structure. The distorted-twisted octahedral square bipyramidal geometric-shape induces a difference in the crystal field splitting energy compared to that of the perfect octahedral square bipyramidal geometric-shape.