使用熱輔助密度泛函理論對n-triangulene之電子性質的理論研究

Abstract

此論文中，我使用密度泛函理論研究三角稀(triangulene)及其衍伸系統(ntriangulene)，依據結果顯示，若使用傳統密度泛函理論計算延伸三角稀，系統基態時將具備高自旋量子數(spin number) ， 然而由於自旋汙染(spincontamination)，傳統泛函理論將無法良好取得低自旋下的能量，因此，我另外使用熱輔助密度泛函理論(Thermally-Assisted-Occupation densityfunctional theory)對延伸三角稀做計算，根據熱輔助泛函理論的結果，所有的延伸三角稀都得基態都為單重態，且計算中皆沒有自旋汙染的發生，另外，隨著三角稀系統逐漸放大(n)，系統的孤對電子數也會逐步增加(n-1)。 依據延伸三角稀(n=21)的能量狀態密度(Density of states)顯示，此系統具有一堆表面態(Surface state)集中在費米能階(Fermi-level)附近，這些表面態的軌道佔據數(Orbital occupied number)皆為半滿，另外，隨著延伸三角稀的尺寸放大，系統的能隙將逐步縮小，除了基態性質，延伸三角稀的單重態和三重態差距，游離能，電子親和力，基本能隙也在論文中透過熱輔助密度泛函理論計算得到，其中，對於所有的延伸三角稀而言，其單重態和三重態差距皆非常小，再次驗證了簡併態確實在延伸三角稀中存在，也說明了熱輔助密度泛函理論在此系統的重要性。

The electronic properties of n-triangulene have been investigated using Kohn-Sham density functional theory (KS-DFT) and Thermally-Assisted-Occupation density functional theory (TAO-DFT) which is believed to have a correct treatment of strong correlation systems. The results in this study suggest that n-triangulene belong to repulsive Hubbard model and the ground state spin number will follow Lieb’s theorem in KS-DFT calculation. However, the results also indicate severe spin contamination in KS-DFT calculation which will cause inaccuracy about 10 kcal/mol. In TAO-DFT calculation, the results in this study suggest that n-triangulene belong to attractive Hubbard model and it will be singlet ground state for all n-triangulene. In TAO-DFT,the symmetry breaking effect was excluded due to negligible different between restricted singlet state energy and unrestricted singlet state energy (RS-US). Further, results from TAO-DFT calculation predict that there will be (n-1) delocalized lone pair electrons for n-triangulene, which is in consistent with results from Lewis electron dot structure. The Density of States (DOS) of n-triangulene (n=21) using TAO-DFT was plot. In the plot, there were cluster of surface states concentrate at the Fermi-level with their occupied numbers to be half filled. In this study, it was also shown that bandgap of n-triangulene will decrease when size of n-triangulene increases. Beside ground state properties, singlet-triplet (ST) gap, ionization potential (IP), electron affinity (EA) and fundamental gap were also calculated using TAO-DFT. The ST gap for n-triangulene were negligible small, which indicates the degenerated states at Fermi-level and further justify the use of TAO-DFT here.