- 學位論文
以密度泛函理論研究類胡蘿蔔素及其延伸系統之電子性質
Theoretical studies of electronic properties of carotenoids related systems using thermally-assisted-occupation density functional theory
摘要
在這篇論文中，我們以密度泛函理論研究三種類胡蘿蔔素 (Carotenoid)，包含 β 胡蘿蔔素、茄紅素 (Lycopene) 與 γ 胡蘿蔔素與其相關的分子結構。然而，由於 傳統密度泛函在較大的共軛結構這類強關聯系統會出現誤差，導致無法準確地取 得能量，而高階第一原理計算在計算大分子系統又過度費時且不切實際。因此， 我們使用溫度輔助密度泛函理論 (Thermally-Assisted-Occupation density functional theory) 研究共軛鏈上有 1 到 12 個異戊二烯 (isoprene) 的類胡蘿蔔素衍生結構。 由 TAOLDA 的計算結果顯示所有的類胡蘿蔔素及其衍生結構的基態都是單態， 且單態與三重態的能量差、游離能、基本能隙隨著鏈長的長度增加平緩減小;而 電子親和力和對稱化馮諾伊曼熵 (symmetrized von Neumann entropy) 則是逐漸地增 加。而這些分子基態的軌道佔據數 (orbital occupation number) 隨著系統的增大而 出現分數的軌道佔據數，這也指出了這些系統的多重自由基 (multi-radical) 特性， 更加證實了由 TAODFT 計算的正當性。
並列摘要
The electronic properties of ncarotenoids (i.e. βcarotene, γcarotene, and lycopene) have been investigated by using the KohnSham density functional theory (KS-DFT) and ThermallyAssistedOccupation density functional theory (TAO-DFT) which is believed to have a very efficient method for strong correlation system. The results in this study suggest that carotenoids exhibit polyradical character when the polyenechain is consid erably large. With the increase of terpenechain length, the singlettriplet gaps, vertical ionization potentials, and the fundamental gaps decrease monotonically, while the vertical electron affinities ane symmetrized von Neumann entropy increase monotonically. In addition, on the basis of the calculation of orbitals and their occupation numbers, the longer polyenechain are shown to have increasing polyradical character in their ground state, where the active orbitals are found to be delocalized along the length of the polyenechain of the carotenoids.