小富勒希的電子性質理論研究

Theoretical study of electronic properties of small fullerenes

黃堉嘉(Yu-Jia Huang)

指導教授 ： 蔡政達

國立臺灣大學/理學院/物理研究所/碩士(2014年)

https://doi.org/10.6342/NTU.2014.10418

摘要

本篇論文利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)下研究小富勒希(Fullerene)系統的電子性質。小富勒希系統的強關聯(Strongly-correlated)特性造成科沈密度泛函理論(Kohn-Sham density functional theory，KS-DFT)的靜態關聯誤差(Static
correlation error，SCE)，靜態關聯誤差使科沈密度泛函理論計無法正確計算強關聯系統的電子性質。另一方面，高階第一原理計算雖然可以解決強關聯系統的誤差，但其計算耗費的時間與資源並無法應用至大量計算富勒希的同分異構物上
。熱輔助佔據密度泛函理論能在孔沈密度泛函理論同階的計算資源下大幅減低靜態關聯誤差，因而在本篇論文利用來計算大量小富勒希的電子性質。

所有小富勒希的單重態三重態能量差(Singlet triplet energy gap)皆為正，大多在10 kcal/mol下，最大也不超過20 kcal/mol。單重態三重態能量差和根本能量差(Fundamental gap)呈現強烈正相關，而單重態三重態能量差和對稱馮諾伊曼(symmetrized Von Neumann entropy)則呈現強烈負相關性，顯示單重態三重態能量差跟靜態關聯誤差的負相關。相對能量、電子親和力、游離能則未跟其他電子特性成強烈相關性。由自然軌道佔據數和對稱馮諾伊曼熵可以指出富勒希的多重參照性(multi-reference)。

關鍵字

富勒希 ； 熱輔助佔據密度泛函理論 ； 靜態關聯誤差 ； 強關聯系統

並列摘要

Thermally-assisted-occupation density functional theory (TAO-DFT) in local density approximation (LDA) is used to investigate the electronic porperties of small
fullerenes in this thesis. The Strongly-correlated (SC) character of small fulerenes results in the static correlation error (SCE) in Kohn-Sham DFT (KS-DFT), and the SCE makes KS-DFT can not correctly handle the electronic properties of SC systems. On the other hand, high level ab initio methods do consider the correlation, but their
highly computational cost in time and resoureces makes them unapplicable to large number of fullerene isomers. TAO-DFT consumes silmilar cost compared to same level of KS-DFT but reduces considerable SCE in KS-DFT, therefore is applied to study the electronic properties of numerous small fullerenes.

All singlet triplet energy gap of small fullerenes are positive, most of them are smaller than 10 kcal/mol, and none is higher than 20 kcal/mol. Singlet triplet energy gaps have strongly positive correlation with fundamental gaps and singlet triplet energy gaps have strongly negative correlation with symmetrized von Neumann entropies, which indicates the negative correlation between singlet triplet energy gaps and SCE. There are no clear dependence between relative energies, ionization potentials and electron affinities. The multi-reference character of small
fullerenes can be indicated by natural orbital occupation numbers and symmetrized von Neumann entropies.

並列關鍵字

Fullerenes ； Thermally-assisted-occupation density functional theory (TAO-DFT) ； Static correlation error (SCE) ； Strongly correlated system

參考文獻

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