二階超極化率與雙自由基在多並苯中的關係之理論研究

Theoretical study on the relationship between the static second hyperpolarizability and the diradical character in polyacene

林冠宏(Guan-Hung Lin)

指導教授 ： 金必耀

國立臺灣大學/理學院/化學研究所/碩士(2017年)

https://doi.org/10.6342/NTU201701650

摘要

在 1970 年代就發現有機共軛分子有著 pi-pi 電子的作用力，導致有著較大的二階超極化率，且有機共軛分子的結構 (例如: 邊界形狀有分成扶手椅型 (armchair) 和鋸齒狀型 (zigzag)) 也扮演很重要的角色影響著二階超極化率，因此了解不同結構有機共軛分子的二階超極化率是件重要的課題。在十幾年前已經有文章指出鋸齒狀-石墨烯奈米帶(zigzag-graphene nanoribbon) 的結構有電子會定域在邊界，這些電子就像是自由基的形式，想了解因為鋸齒狀結構所產生的自由基如何影響著二階超極化率。多並苯 (Polyacene) 可以視為最窄的鋸齒狀-石墨烯奈米帶，一樣也有電子會定域在邊界的性質，同時擁有 pi-pi 電子的未定域的特性與自由基定域在邊界的特性會怎麼影響二階超極化率。有兩種方法定義“雙自由基性質 (y)”。第一種方法在 1971 年E.F.Hayes 要做configuration interaction (CI) 計算，但 CI 的計算需要大的計算量和時間，所以在 1975 年由 Kizashi Yamaguchi 用 unrestricted Hartree-Fock 定義出“雙自由基性質 (y)”，減少的計算量與時間。想藉由“雙自由基性質”了解多並苯分子中，自由基與二階超極化率之間的關係。(1) 一開始，先用 Hubbard modol 改變參數 U 和 t 在兩電子系統去理解“雙自由基性質”，可以透過改變“雙自由基性”去改變躍遷偶極矩，但同時也會影響組態的能量，躍遷偶極矩和激發的能量兩者對於二階超極化率分別為正比、反比，所以可以將二階超極化率寫“雙自由基性質”的函數，在某個臨界值以下，二階超極化率是由激發的能量所為主要貢獻; 在某個臨界值以上，二階超極化率是由躍遷偶極矩所為主要貢獻，藉由 y 可以知道在不同的程度的條件下，二階超極化率是由不同因素所控制的。(2)PPP model 可以很好可以描述純碳的共軛系統，用 PPP model 來描述多並苯，可以發現多並苯有著較明顯的“雙自由基性質”，“雙自由基性質”跟邊界形狀有關也和分子的大小有關，隨著多並苯的尺寸變大電子定域在邊界的特性越明顯。已知二階超極化率跟尺寸大小成高次方正比，所以每一單元下的二階超極化率才是我們所關注，對多並苯的大小與每一單元下的二階超極化率，可以發現 n=14 每一單元下的二階超極化率對達到一個最大值，再隨著尺寸變大每一單元下的二階超極化率會漸漸變小，我們的結果顯示 pi-pi 電子的未定域化被受到自由基會定域在邊界而侷限導致每一單元下的二階超極化率會漸漸變小。

關鍵字

二階超極化率 ； 雙自由基 ； 多並苯

並列摘要

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.

並列關鍵字

second hyperpolarizability ； diradical character ； polyacene

參考文獻

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