| Summary: | 碩士 === 國立臺灣大學 === 化學研究所 === 105 === In 1962, Terhune et al. first discovered electrical-field-induced second harmonic generation. Hermann and Ducuing put their research focus on second hyperpolarizability of long-chain conjugated hypercarbon in 1970s. After Hermann and Ducuing, more and more people have devoted on the second hyperpolarizability of conjugated organic molecules. They have shown that conjugated organic molecules usually present larger second hyperpolarizability because of pi-pi electrons delocalization. Zigzag-graphene nanoribbons (zGNRs) is common conjugated organic molecules. In addition, z-GNRs have been reported predicted localized electron on the edge. After these studies, several theoretical papers have reported these electrons are like radicals. The electronic properties of radicals species have already received considerable attention. There are two methods to define the diradical character. One is through configuration interaction (CI) calculation by Edward F. Hayes in 1971 and the other is through unrestricted Hatree-Fock (UHF) to construct unrestricted natural orbital (UNO) and do CI calculation for the singlet ground state open-shell molecules by Kizashi Yamaguchi in 1975.(1)First, in the simplest two-site Hubbard model, it has shown that the numerical solution of the second hyperpolarizability can be rewritten by the diradical character and we realize that the transition dipole moments or the excitation energies at different cases dominate the second hyperpolarizability.(2)Following by the two-site Hubbard model, we use PPP model to describe the polyacene. The polyacene can be view as the narrowest zigzag graphene nanoribbons (z-GNRs). As the size of polyacene is larger, the more radicals localize on the edge. Polyacene both have pi-pi electrons delocalization and also have edge effect. We want to realize the variation of the second hyperpolarizability with increasing size of polyacene. Because the second hyperpolarizability depend on the size of molecules, it is necessary to adjust the size of polyacene. There is a maximum of gamma/unit cell at n=14. After n=14, gamma/unit cell get decaying as the size of polyacene enhances. The pi-pi electron delocalization The edge effect making gamma/unit cell decaying results from repressing the pi-pi electrons delocalization.
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