In the current research, it is explained the optical properties of both cases doped and undoped graphene nanoribbons. These properties depend critically on a number and type of impurity are founded in the ribbon (the width and the nature of the ribbon edge are constants). Finally, the calculation has involved optical properties of all paradigms such as geometrical structure, HOMO, LUMO, total energy, Fermi level energy, binding energy, work function, polarizability and hyperpolarizability respectively of each the structures studied. Herein, the both 8Al-GNR and 8P-GNR are the highest reactivity structures among all specimens (viz 1046.008 and 1035.1623 a.u) respectively. The results elucidate that the first hyperpolarizabilities of GNRs paradigms before and after doped were 0.0354 esu and 2855.87 esu, respectively. The results bring to light that the effect of contaminations is to greatly increase the hyperpolarizability value. The high values of polarizability and hyperpolarizability exhibit that the paradigms have very useful linear and nonlinear optical implementation as well as , the computation has included of the values of wavelength of maximum emission , vertical excited of energy , oscillator strength , optical energy gap , and cases of major electronic transition, where each studied paradigms were simulated using TD-DFT with B3LYP/6-31G (d, p). Interestingly, the optical band gap was evaluated of pristine GNRs and found equal to 0.6256 eV. Whereas, the value of doping in GNR can be noted that the band gaps are sometimes shrinks and other times expands. These values are determined between (0.1018 eV to 1.276 eV) for paradigms 2Al-GNR and 4P-GNR respectively. Finally, the band gaps cover a wide range of values and thus allows it to be used widespread in optical and electronic applications.

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