以密度泛函理論研究石墨烯相關系統之電子性質

Abstract

在這篇論文裡,我們以密度泛涵理論研究與石墨烯(Graphene)相關的分 子結構, 包括石墨烯奈米片(Graphene-like Nanopatches)和聚合薁鏈(Fused-Azulene chain), 特 別 是 這 些 聚 合 物 的 單 重 態 和 三 重 態 能 量 差 距(singlet and triplet energy gap), 並且利用非線性最小平方法(Non-linear least squares method)推算該聚合物在尺寸極限下單重態和三重態能量差距。 我們發現石墨烯奈米片和聚合薁鏈在尺寸極限下的單重態和三重態能量差距非常小。 另外我們也研究了這些分子基態的軌道佔據數(orbital occupation number),其最高被佔據軌道(highest occupied molecular orbital)的電子數和最低沒有被佔據軌道(lowest unoccupied molecular orbital)的電子數隨著分子系統的尺寸增加而越來越接近 1。 進一步研究之後,我們更發現不僅最高被佔據軌道和最低沒有被佔據軌道具有這種趨勢,其他附近的分子軌道也具有相同的趨勢,代表石墨烯奈米片和聚合薁鏈擁有多重自由基(multi-radical)的特 徵使用的是開發版本的化學計算軟體Q-Chem (Ab initio quantum chemistry package)。

The electronic properties of fused-azulenes chain and graphene-like nanopatches have been probed by using the Thermally-Assisted-Occupation density functional theory (TAO-DFT) which is believed to have a correct treatment of such strong electronic correlation systems. The results in this study suggest that not only fused-azulenes but also graphene-patches show polyradical characteristics in their respec-tive polymeric limits, and also predict almost vanishing singlet-triplet states energy gaps of them by extrapolating the singlet-triplet states energy gap to their respective infine size limits. The theoretical calculation results of DFT provides a irregular trend of singlet-triplet energy gap curve for both fused-azulenes and grapehen-patches. We compared the singlet-triplet energy gap curves calculated by DFT and TAO-DFT, TAO-DFT provides a more reasonable and more smooth curve than DFT since TAO-DFT accurately describes the strong correlation effect and reduce the spin contamination effectively.