Theoretical Investigations Of The Structures, Stabilities, And Electronic Properties Of Metal Clusters, Fullerenes And Their Derivatives

Predicting and designing novel chemically inert cluster species that could be promising for making new cluster assembled nanostructured materials is a leading thread in current research. In this thesis, we try to explore Al-doped Pb clusters with high stabilities. Besides, we investigate the structures, stabilities, electronic properties, and optical properties of C₅₂, C₅₆, C₅₈, and C₆₈ fullernes, which violating the IPR rule. We also study the structures and electronic properties of fullerene derivatives based on C₅₆ and C₅₈, and compated to experiments.(1) Density functional theory based methods have been used to calculate the global equilibrium geometries and electronic properties of neutral AlPbn and cationic AlPb_n⁺ clusters (n=1-12). Several cationic clusters such as AlPb9+, AlPb₁₀⁺, and AlPb₁₂⁺ with enhanced stabilities have been found. To assess the special stability of C_3v AlPb₉⁺ and D4d AlPb₁₀⁺, the molecular orbitals analyses have been performed, and the result shows that its large stability may arise from their spherical aromaticity and large nucleus-independent chemical shifts (NICS) values. The big cavity and large NICS values of D4d Pb₁₀^2- suggest that it can encapsulate other appropriate metal atoms successfully. Additionally, the nine-atom Pb clusters Pb₉^2-, Pb₉^3-, and Pb₉^4- possess strong aromatic character. Especially, the Pb₉^4- cluster exhibits double spherically aromatic character and the largest NICS value at the center of the cage. Besides, we analyze the electronic properties and stabilities of cationic MPb₁₂⁺ clusters (M = B, Al, Ga, In, and Tl). The structures of MPb₁₂⁺ with icosahedral (I_h) symmetry are energetically favorable, and their high stabilities are also related to their spherical aromaticity and large NICS values. Furthermore, the vertical ionization potentials of the neutral MPb₁₂ clusters are smaller than that of some alkali metal atoms, indicating that the neutral MPb₁₂ clusters possess superalkali character. We also provide the first quantitative evidence for the existence of"d orbital aromaticity"in Sn₁₂^2- and Pb12^2- clusters. The nucleus independent chemical shifts (NICS) of Ih Sn₁₂^2- and Pb12^2- are -5.0 and -20.7 ppm, respectively, based on B₃LYP/aug-cc-pVDZ(-PP) predictions.The startling conclusion is the NICS_4d of Sn12^2- and NICS5d of Pb12^2- are ?5.0 and ?7.5 ppm, respectively, suggesting that their inner d orbitals contribute significantly to the total NICS values.(2) PM3 method together with density functional theory based methods is employed to perform the calculations of C₅₂, C₅₆, C₅₈, and C₆₈ fullerenes. C₅₂(C₂:029), C₅₆(D₂:003), C₅₈(C_3v:0001), and C₆₈(C₂:0112) with the least adjacent pentagons are predicted to be the most stable fullerene isomers. However, there are also some neutral isomers violate the PAPR. Further investigations show that not only the structural effects (via the PA number) but also the electronic effects (due to the aromatic character) determine the energy order of different isomers. To clarify the relative stabilities of the fullerene isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy, and the results show that each of the most stable fullerene isomer behaves more thermodynamically stable than other C₅₂, C₅₆, C₅₈, and C₆₈ fullerenes isomers, respectively. The infrared spectra of some most stable fullerene isomers are predicted to facilitate future experiments. The static second-order hyperpolarizabilities of the fullerene isomers are slightly larger than that of C₆₀. We found that the pentagon adjacency penalty rule (PAPR) does not necessarily apply to the charged fullerene cages. Take C₆₈ for example, C₆₈(C)2:0112) possesses the lowest energy of all the neutral isomers. However, as to C₆₈^2-, C₆₈^4-, and C₆₈^6- fullerenes, the isomers C₆₈^2-(Cs:0064), C₆₈^4-(C_2v:0008), and C_{68<sup>6-(D3:0009) respectively, are predicted to be the most stable. The vertical electron affinities of the neutral Cs:0064, C2v:0008}, and D₃:0009 isomers are 3.41, 3.29, and 3.10 eV, respectively, suggesting that they are good electron acceptors. Besides, we found that the fullerenes can be stabilized with encapsulation of metal atoms and small clusters, of which the interaction between inner metal atoms (or small cluster) and outer cage greatly releases the strain of structure.(3) The geometries of carbon cages (fullerenes) is governed by the isolated pentagon rule (IPR), which states that the most stable fullerenes are those in which all pentagons are surrounded by five hexagons. However, it is impossible for fullerenes in the range from C₂₀ to C₅₈ and from C₆₂ to C₆₈ to obey it. Owning to the high strain of the non-IPR fullerenes with unavoidable adjacent pentagons, these small fullerenes are predicted to be highly instable and difficult to isolate. One way to stabilize these fullerenes is rehybridization change of some carbons in pentagons from sp² to sp³ upon chlorination (fluorination or hydrogenation), such as C₅₀Cl₁₀, C₅₈F₁₈, and C_{64H4. In this paper, we investige the fullerene derivatives based on C56 and C58.The most stable fullerene derivatives C56Cl}8 and C₅₆Cl₁₀ based on the parent fullerene C₅₆(C_2v:011), rather than the ones from the most stable C₅₆ isomer with D₂ symmetry, are predicted to possess the lowest energies, and they are highly aromatic. Further investigations shows that the heats of formation of the C₅₆Cl₈ and C₅₆Cl₁₀ fullerene deriavatives are highly exothermic, that is, -48.59 and -48.89 kcal/mol per Cl₂, suggesting that adding 8 (or 10) Cl atoms releases much of the strain of pure C₅₆(C_2v:011) fullerene and leads to large stabilities of the derivatives. Besides, the ¹³C NMR chemical shifts and infrared spectra of C₅₆Cl₈ and C₅₆Cl₁₀ are simulated to facilitate future experimental identification. Similarly, we have studied the stabilities and electronic properties of two different structures C₅₈X₁₈ (A) and C₅₈X₁₈ (B) where X = H, F, and Cl. The large energy gaps between the highest occupied molecular orbitals and the lowest unoccupied molecular orbitals (between 2.64 and 3.45 eV) and the aromatic character (with nucleus independent chemical shifts from -10.0 to -13.9 ppm) of C₍58X18 (A) and C₅₈X₁₈ (B) indicate that they possess high stabilities. Further investigations show that the heats of formation of C₅₈X₁₈ fullerene derivatives are are also highly exothermic, suggesting that the adding of 9 X₂ releases much of the strain of pure C₅₈ fullerene and leads to stabilities of the derivatives. Compared to the C₅₈F₁₈ (B) which has been experimentally characterized, C₅₈F₁₈ (A) possess lower energy and stronger aromatic character and it should also be isolated.In summary, to stabilize the fullerenes vilating IPR, we should release the strain pertaining to the adjacent pentagons in the fullerene structure. There are two methods: One way is to add hydrogen or halogen atoms to the surface of fullerene, which will release the strain and finally get the stable fullerene derivatives. The second way is to encapsulate appropriate atom or cluster into the cage structure. The interaction of inner cluster (or atom) and outer cage will lower the energy of system, and we will get stable metallofullerene. The size affect of inner cluster is important to effectively stabilize the fullerene. The electronic properties of the resulting fullerene derivatives and metallofullerene are greatly different from those of their parent fullerene, which maybe enable them as candidates of materials with different properties.