- 學位論文
以熱輔助佔據密度泛函理論探討六角形奈米石墨烯環之電子結構
TAO-DFT Investigation in Electronic Properties of unit-width Hexagonal Graphene Quantum Rings
摘要
由於傳統科恩－沈密度泛函理論(Kohn-Sham Density functional theory) 在計算強關聯電子系統上並無法達到令人滿意的表現，有許多研究試圖尋找更有效的計算方法。而在多參考組態相互作用方法(multi-reference configuration interaction method) 的架構下，雖然能解決強關聯電子系統問題，但卻由於計算複雜度過大，導致只能計算相對小的系統，在實際應用上非常有限。熱輔助佔據密度泛函理論因此被提出以解決此問題，並由於其計算複雜度與柯恩-沈理論相近，在相同計算資源下，我們能獲得更加可信的結果。在此篇論文中，我們以局域密度近似(local density approximation) 下的熱輔助佔據密度泛函理論計算六角形量子石墨烯環之電子結構隨尺寸增大之特性變化(邊長n=3-15)。我們發現其在計算上能夠保持自旋對稱性，改善科恩-沈對稱性破壞的問題，並在電子游離能與電子親和力的計算上，完成了科恩-沈方法無法完成的計算。我們數值計算的結果預測六邊形石墨烯環的基態為單重態，並有隨尺度增大而減小的單重-三重態能階差，游離能，與隨尺度增大的電子親和能和馮紐曼熵。我們也觀察到此系統由小尺度的非自由基特性逐漸過渡到大尺度的自由基特性。
並列摘要
Reliable prediction of the ground state electronic properties of graphene nano-systems has been very challenging for conventional computational methods such as the popular Kohn-Sham Density functional theory (KS-DFT), due to the presence of strong static correlation effect. Thermally-assisted-occupation density functional theory (TAO-DFT) has thus been developed to tackle this problem. TAO-DFT has similar computational cost to KS-DFT, but is shown to improve KS-DFT for multi-reference systems even at simplest level local density approximation (LDA), and found to be in good agreement with the existing experimental and high-level ab initio data for several systems. Inspired from previous work on Aharonov-Bohm (AB) effect in graphene quantum rings (GQRs), in this work we numerically study electronic properties of zigzag-edged unit-width hexagonal graphene quantum rings (HGQRs) as a function of size (n=3-15) using TAO-DFT at LDA level, finding monotonic decreasing singlet-triplet gaps, vertical ionization potentials, and fundamental gaps with size, while monotonic increasing vertical electron affinities and symmetrized von Neumann entropy. We demonstrate n-HGQRs show a smooth transition from non-radical to poly-radical nature as size increases. We further found that TAO orbital occupation numbers (TOONs) shows a six-level grouping behavior, which might arise from its six-fold rotational symmetry. However, this grouping is not not seen in previous TAO-DFT calculation on hexagonal graphene nanoflake because of the strong coupling between each segment.