- 學位論文
石墨烯奈米帶和環狀並苯的多自由基特性
Polyradical Characters of Graphene Nanoribbons and Cyclacenes
摘要
Kohn-Sham密度泛函(KS-DFT)在較大的石墨烯奈米帶(GNRs)和環狀並苯上會出現靜態關聯性誤差(SCE)。這個誤差會影響計算單重態和三重態能量的準確性。高階第一原理方法可以處理電子關聯性作用，但對於大分而言卻是費時且不切實際。有效率地處理處理此類系統是很重要的。我們研究到50個聯苯單位構成的石墨奈米帶和100個苯單位構成的環狀並苯。我們使用溫度輔助占據密度泛函理論(TAO-DFT)，在局部密度近似(LDA)下來探討這些共軛系統統。TAO-DFT採用Fermi-Dirac 分布模擬強關聯系統的多參考特性。所有TAO-DFT的計算結果都顯示單重態是基態。石墨烯奈米帶的單重態和三重態能量差平緩減少，但是環狀並苯卻在一開始時出現震盪。兩個系統的能差在無限長的情況下可被推估小於0.11 kcal/mol。兩個系統的軌域占據數都出現分數。石墨奈米帶很明顯在1.2和0.9之間聚集，而環狀並苯卻是伴隨著週期性震盪慢慢靠近1。自由基指標結果指出這兩個系統的自由基特性。對稱von Neumann熵可以指出分子的多參考特性。TAO-LDA可以減少SCE且提供更好單重態和三重態能量差的趨勢。
並列摘要
For large Graphene nanoribbons (GNRs) and cyclacenes, Kohn-Sham density functional theory (KS-DFT) has static correlated error (SCE). This error affects the accuracy of singlet and triplet energy. High level ab initio methods handle electronic correlation well, but the cost is too high for large molecules. An efficient method is very important. We study nearly 50 fused biphenyl units of GNRs and 100 fused benzene units of cyclacenes. We use thermally-assisted-occupation density functional theory (TAO-DFT) in local density approximation (LDA) for these pi-conjugated systems. TAO-DFT using Fermi-Dirac distribution simulates multi-reference characters for strong correlated systems. All singlet-triplet energy gaps by TAO-LDA indicate singlet ground states. The EST gaps decrease smoothly for GNRs. The singlet-triplet energy gaps decrease initially with oscillations for cyclacenes. The singlet-triplet energy gaps at infinite is within 0.11 kcal/mol for both systems. The restricted occupation numbers become fractional for both. The occupation numbers of GNRs collect between 1.2 and 0.9 obviously. The occupation numbers of cyclacenes slowly come to 1 with periodic oscillations. The radical index indicates polyradical characters of both systems. The symmetrized von Neumann entropy also indicates multi-reference characters. TAO-LDA can reduce SCE and provides better trends of singlet-triplet energy gaps.