使用熱輔助佔據密度泛函理論對融合薁並苯之電子性質的理論研究

Abstract

本論文使用熱輔助佔據密度泛函理論 (thermally-assisted-occupation density functional theory, TAO-DFT) 在局部密度近似 (local density approximation, LDA) 下研究融合薁並苯 (fused azulene-acene) 系統的電子性質，並與其同分異構物並苯 (acenes) 比較。若使用孔沈密度泛函理論 (Kohn-Sham density functional theory, KS-DFT) 計算融合薁並苯系統，會產生因其強關聯 (strongly correlated) 特性而發生的靜態關聯誤差 (static correlation error, SCE)，得到物理上不正確的三重態基態 (triplet ground state)。另一方面，孔沈密度泛函理論的計算過程中容易收斂到局域最小值，因此必須用大量初始條件和算法才能得到全域最小值，相較之下熱輔助佔據密度泛函理論能有效收斂到絕對最小值且修正靜態關聯誤差，同樣的計算資源下更有效率，因此本篇論文使用熱輔助佔據密度泛函理論來研究融合薁並苯系統的電子性質。 在短鏈 (n<8) 融合薁並苯系統中使用基於孔沈密度泛函的混成泛函B3LYP得到負的單重態三重態能量差 (Singlet-Triplet gap)，而使用熱輔助佔據B3LYP的計算結果皆為正，也就是單重態基態。在局部密度近似下，長鏈 (n<75)的融合薁並苯的單重態三重態能量差皆小於並苯的能量差，得知兩端融合七五環可以將其降低，且減少幅度隨著長度增加而減少。從對稱馮諾伊曼熵 (symmetrized von Neumann entropy) 和軌域佔據數可以得知融合薁並苯的多重參考性 (multi-reference)，且從對稱馮諾伊曼熵對於鏈長的關係發現融合薁並苯與並苯斜率相同向上平移，發現融合薁並苯的軌域佔據數結構與並苯的類似。

In this thesis, we investigate the electronic properties of fused azulene-acene system using thermally-assisted-occupation density functional theory (TAO-DFT) in local density approximation (LDA) and compare to the properties of its isomer, acenes. If we use Kohn-Sham density functional theory (KS-DFT) to calculate, we get unphysical triplet ground state because of static correlation error (SCE) causing by the strong correlated (SC) character of fused azulene-acene. On the other hand, the energy usually truncate to local minimum during the iterating process of KS-DFT, and thus it needs lots of initial guess and algorithm to find the global minimum. TAO-DFT can effectively truncate to global minimum and correct SCE under the same computational resource, therefore is used to calculate the properties of fuse azulene-acene. Negative singlet-triplet energy gap is obtained using hybrid functional B3LYP based on KS-DFT for fused azulene-acene in short length (n<8). The result is positive, namely siglet ground state, using TAO-B3LYP. In LDA, singlet-triplet gaps of fused azulene-acene are all lower than ones of acenes. We can know that fusing the 7, 5 rings will lower ST gap, and the degree of reduction decrease as the length increase. Symmetrized von Neumann entropy and orbital occupation numbers show the multi-reference character of fused azulene-acene. The slope of fused azulene-acene of symmetrized von Neumann entropy to length is the same as one of acenes and translate upward, which indicates fused azulene-acene has similar structure of orbital occupation numbers to acenes.