The structure and optical properties of a set of R-1,1´-binaphthyl-2,2´-dithiol (R-BINAS) monosubstituted A-Au₃₈(SCH₃)₂₄ clusters are studied by means of time dependent density functional theory (TD-DFT). While it was proposed earlier that BINAS selectively binds to monomer motifs (SR-Au-SR) covering the Au₂₃ core, our calculations suggest a binding mode that bridges two dimer (SR-Au-SR-Au-RS) motifs. The more stable isomers show a negligible distortion induced by BINAS adsorption on the Au₃₈(SCH₃)₂₄ cluster which is reflected by similar optical and Circular Dichroism (CD) spectra to those found for the parent cluster. The results furthermore show that BINAS adsorption does not enhance the CD signals of the Au₃₈(SCH₃)₂₄ cluster.