DFT calculations; Green synthesis; radial breathing modes; Raman in nanoparticles; Ti nanoparticles Density functional theory; Energy dispersive spectroscopy; Nanoparticles; Optical properties; Titanium; X ray spectroscopy; Energy dispersive X ray spectroscopy; Green synthesis; Metallic nanoparticles; Opuntia ficus indica; Radial breathing mode; Titanium nanoparticles; Transmission electronic microscopies; Vibrational parameters; Synthesis (chemical)