利用電荷自洽密度泛函緊束縛方法探討導電高分子和碳奈米結構的幾何、電性和振動性質

Geometric, electronic, and vibrational properties of conductive polymers and carbon nanostructures studied using the SCC-DFTB method

李文凡(Wun-Fan Li)

指導教授 ： 魏恆理

國立交通大學/理學院/應用化學系所/碩士(2009年)

https://doi.org/10.6842/NCTU.2009.00304

摘要

電荷自洽密度泛函緊束縛方法（以下簡稱SCC-DFTB）已被成功地應用在不同的化學系統的結構，電性，和振動性質上:１.共軛雜環高分子， 2.奈米鑽石， 3.多環芳香族化合物-石墨片和HPB分子， 4.單層和多層富勒烯， 5.奈米碳管。我們觀察了一些新的題目。１.對於共軛雜環高分子的研究，包括順－反式聚乙炔，聚環戊二烯，聚吡咯，聚呋喃，和聚噻吩。我們探討了能階差，電子態密度，偶極矩，四極矩和極化率等等的性質。這些性質整體而言呈現了收斂的行為。２. 對於奈米鑽石，我們計算了四面體和八面體結構之奈米鑽石的拉曼光譜。這些光譜擁有實驗得到之鑽石拉曼光譜特有的位於1332 波數的訊號。３.多環芳香族化合物的拉曼光譜已經以電荷自洽密度泛函緊束縛方法計算得到。４.我們已經計算得到了單層富勒烯的電子和振動性質。我們也探討了內嵌水分子和乙炔之富勒烯包合物的振動光譜。我們發現如果外層的富勒烯足夠大，則裡面分子的振動光譜訊號會完全被外層富勒烯遮蔽。５.我們運用了兩種不同的SCC-DFTB分散力模型計算了 的位能面.這兩種分散力模型分別是Slater-Kirkwood形式和Lennard-Jones形式。在以Lennard-Jones模型得到的結果中， 轉動的能障僅僅只有１.62 Kcal/mol。這指明在室溫之下， 能在 裡面自由轉動，並且位能面上存在許多局部的最小值。對於多層富勒烯之0結構的研究結果和 的位能面研究一致：對於只有單層差距的多層富勒烯（ ， ，和 ），內層富勒烯會坐落在中心點。而對於更大層距的多層富勒烯（ ， ，和 ），內層富勒烯傾向停留在外層富勒烯壁的附近。多層富勒烯之振動光譜的結果和富勒烯包合物的結果相似。這些光譜指出，只要外層富勒烯的尺寸足夠大，內層富勒烯的訊號就會被遮蔽。５.我們計算了不同尺寸和長度之扶手椅型單層奈米碳管的的拉曼光譜。即使是在此研究中最長的碳管模型：15奈米的（5,5）單層奈米碳管，朝著實驗所得之單層奈米碳管拉曼光譜的收斂仍未達到。目前的研究闡述了SCC-DFTB方法對於研究大分子性質和這些性質收斂至固態材料的能力和限制。

關鍵字

電荷自洽密度泛涵緊束縛方法 ； 紅外光譜 ； 拉曼光譜

並列摘要

The SCC-DFTB method has been applied for studying the geometrical, electronic, and vibrational properties of various chemical systems. The systems can be divided into following categories: 1.conjugated heterocyclic polymer chains, 2.nanodiamonds, 3.polycyclic aromatic hydrocarbons (PAHs) including graphene flakes and hexa-peri-benzacoronenes (HPBs), 4.single and multi-shell fullerenes and, 5.carbon naotubes. Several new topics have been investigated. 1. The study on the conjugated heterocyclic oligomer chains, including trans-cisoid polyacetylene, polycyclopentadiene, polypyrrole, polyfuran, and polythiophene, shows overall convergent behavior of ramous properties including HOMO-LUMO gaps, DOS, dipole moment, quadrupole moment and polarizability. 2. For nanodiamonds, the Raman spectra of both series of octahedral and tetrahedral diamonds show an evidence of the unique peak at 1332 cm-1, which was previously observed in experimental Raman spectra of diamond. 3. The Raman spectra of the finite PAHs have been computed out using the SCC-DFTB method. 4. The electronic and vibrational properties of single-shell fullerenes have been calculated. The vibrational spectra of endohedral fullerenes with inserted water and acetylene molecules have been discussed for different size of the encapsulating fullerene. It is found that when the cage is large enough, the signal from the inner molecule is completely shielded by the fullerene cage. The PES of have been scanned with two types of dispersion-corrected SCC-DFTB models, Slater-Kirkwood type and Lennard-Jones type. The energy barrier for to rotate is merely 1.62 Kcal/mol in the LJ scheme, which indicates that can freely rotate at room temperature and there exist many energy local minima in the PES. The geometric structures of multi-shell fullerenes are in accord with the PES study: for the multi-fullerene cages with only one shell difference ( , , and ), the inner fullerene is located in the center. But for the aggregates with larger spacing between shells ( , , and ), the inner fullerenes prefer to stay near the outer cage. Vibrational spectra of the multi-shell fullerenes lead to similar conclusions as those of the endohedral molecule-fullerene complexes. They show that if the cage is large enough, the signal from the inner fullerene is masked. 5. Raman spectra of armchair single–wall carbon nanotubes (SWNT) with different diameters and lengths are presented. The convergence toward the experimental Raman spectra of “infinitely” long SWNT is still not achieved even for the longest studied presently model, i.e. a 15nm (5,5) armchair SWNT. The present study illustrates the capability and limitations of the SCC-DFTB method for studying the properties of large molecules and their convergence toward the corresponding solid state materials.

並列關鍵字

SCC-DFTB ； IR spectrum ； Raman spectrum

參考文獻

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