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We present a real-space formulation for calculating the electronic structureand optical conductivity of such random alloys based on the Kubo-Greenwoodformalism interfaced with the augmented space recursion (ASR) [A. Mookerjee, J.Phys. C: Solid State Phys. {\bf 6}, 1340 (1973)] formulated with theTight-binding Linear Muffin-tin Orbitals (TB-LMTO) basis with vanLeeuwen-Baerends corrected exchange (vLB) [Singh et al, Phys. Rev B {\bf 93},085204, (2016)]. This approach has been used to quantitatively analyze theeffect of chemical disorder on the configuration averaged electronic propertiesand optical response of 2D honeycomb siliphene Si$_{x}$C$_{1-x}$ beyond theusual Dirac-cone approximation. We predicted the quantitative effect ofdisorder on both the electronic-structure and optical response over a wideenergy range, and the results discussed in the light of the availableexperimental and other theoretical data. Our proposed formalism may open up afacile way for planned band gap engineering in opto-electronic applications.

Band-gap tuning and optical response of two-dimensional Si$_x$C$_{1-x}$: A first-principles real space study of disordered 2D materials