| Summary: | 碩士 === 國立臺灣大學 === 物理學研究所 === 107 === 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.
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