藉由熱輔助密度泛函對葉黃素類及其相關系統的電子性質研究

Abstract

葉黃素類(xanthophyll)是類胡蘿蔔素(carotenoid)的其中一種類別，因其經常出現在健康保健食品中最為出名。如果想要使用傳統上最廣為使用的科恩-沈密度泛函理論(Kohn-Sham density functional theory)來處理葉黃素類，會因其為強關聯系統(strongly correlated system)而導致困難。所以我們使用熱輔助密度泛函理論(thermally assisted occupation density functional theory)來求得葉黃素類的相關化學性質。在本篇論文中我們針對四種在工業及學術文獻上較常出現的四種葉黃素類：蝦青素(astaxanthin)，角黃素(canthaxanthin)，葉黃素(lutein)和玉米黃素(zeaxanthin)及其相關系統做研究。相關系統是指我們將碳加入其碳鏈中使其結構中的碳鏈延長而得到的新化合物，我們會另外研究葉黃素類的相關系統是為了更加了解強關聯系統的性質。 我們利用熱輔助密度泛函理論得到了葉黃素類及其相關系統的下列化學性質：單重態與三重態之間的能量差(singlet-triplet gap)，垂直游離能(vertical ionization potential)，垂直電子親和力(vertical electron affinity)，基本能隙(fundamental Gap)和對稱馮紐曼熵(symmetrized von Neumann entropy)等等。

Xanthophylls, a class of carotenoids containing oxygen in its structure, has attracted much attention due to its health-related effect. Because it is a strongly correlated system, we will encounter difficulties using Kohn-Sham density functional theory (KS-DFT) to study xanthophylls. In order to deal with those strongly correlated systems, we will apply the recently established thermally-assisted-occupation density functional theory (TAO-DFT), which has a great performance with strongly correlated systems and have a frequent usage with systems having radical nature. We put our interest in four types of xanthophylls: astaxanthin, canthaxanthin, lutein, and zeaxanthin. For a better understanding of the radical nature and the effect due to this nature, we also study their lengthen systems, in which we add carbon atoms in the conjugate bond and keep the terminal groups unchanged.The electronic properties we have interest in include singlet-triplet gap (ST gaps), vertical ionization potential (IPv), vertical electron affinity (EAv), fundamental gap (Eg), symmetrized von Neumann entropy (SvN), and active orbital occupation numbers. We find that the singlet state is the ground state and that the energy difference between single and triplet become smaller when xanthophylls become longer. The stronger strongly correlated effect has also been found with longer xanthophylls with the proof from symmetrized von Neumann entropy and orbital occupation numbers.