Theoretical Investigations On The Chemical Stability, Electronic Structure And Optical Property Of Non-IPR Fullerene (<C₇₀ ) And Their Derivatives

Since the discovery of I_h C₆₀, along with its macroscopic scaled synthesis, the fullerenes and their derivatives have attracted extensive attention because of their novel and unusual physical and chemical properties. Structural stabilities of fullerenes are often governed by the well-known isolated pentagon rule （IPR）. Except I_h C₆₀, the C_2n cages with C_2n （2n<70） can not satisfy the IPR due to presence of adjacent pentagons in the cage frameworks. As a consequence, these violating-IPR fullerenes are predicted to be neither stable in structures nor isolable in experiments due to the high steric strains and the resonance destabilization pertaining to the adjacent pentagons. Most of the non-IPR fullerenes are not experimentally approachable presently, and therefore, theoretical studies are significant for investigating their structural stabilities and electron properties. In this thesis, a comprehensive investigation on structural stabilities, and electronic properties of some violating-IPR fullerene C_2n （2n<70） and their derivatives are performed by means of quantum chemical method. The main research results are summarized as follows:1. The 89 classical isomers of metallofullerene Ca@C₄₄ have been investigated by means of diverse theoretical methods. Ca@C₄₄ （D₂:53） isomer with eight adjacent pentagons in the cage framework is predicted to possess the lowest energy. Concentration analysis reveals D₂:53 isomer prevails in a wide temperature range. The encapsulation of Ca atom in C₄₄ fullerene is exothermic and the electronic structure of D₂:53 can be described formally as Ca²⁺@C₄₄^2-. Frontier molecular orbitals and density of states for D₂:53 suggest that both HOMO and LUMO are carbonlike with low Ca character. In addition, the vibrational spectrum of Ca@C₄₄ （D₂:53） has been simulated and analyzed to gain an insight into the metal-cage vibrations.2. Stability and electronic property calculations of T_d C₂₈ fullerene and exohedral fluorine and trifluoromethyl derivatives C₂₈F_4-n（CF₃）_n （n=0,1,2,3,4） are performed systematically on the basis of density functional theory. All C₂₈F_4-n（CF₃）_n （n=0,1,2,3,4） have large HOMO-LUMO gaps together with positive values of binding energies, suggesting their high chemcial stable. Analysis of theÏ€-orbital axis vector indicates the high strain in T_d C₂₈ cage could be greatly released by fluorine and trifluoromethyl decorations. Mulliken charge calculation reveals that adding different electron groups to T_d C₂₈ cage can cause remarkably different charge populations. In addition, on the basis of the ionization potential and electron affinity calculations, the C₂₈F_4-n（CF₃）_n （n=0,1,2,3,4） molecules manifest weak redox properties.3. On the basis of density functional theory, the geometrical structures and electronic properties of C₆₈X₄ （X= H, F, and Cl） fullerene compounds has been studied. In all classical C₆₈X₄ isomers with two adjacent pentagons and one quasifullerene isomer [C_s:C₆₈（f）] containing a heptagon in the framework, C_s:0064 isomers are most favorable in energy. The addition reaction energies of C_s:0064 are high exothermic, especially for the case of C₆₈F₄. The C₆₈X₄ （C_s:0064） possess strong aromatic character, with nucleus independent chemical shifts ranging from -22.0 to -26.1 ppm. X attachments lead to large vertical electron affinities （3.29 eV and 3.15 eV, respectively） of C₆₈F₄ and C₆₈Cl4, and therefore, they could be excellent electron acceptors for potential photonic/photovoltaic applications. Finally, the infrared spectra of the most stable C_s:0064 are simulated to assist further experimental characterization.4. Electronic structures and nonlinear optical properties of C_3v C₆₀F₁₈ and D_3d C₆₀Cl₃₀ have been systematically studied. The large energy gaps （3.62 and 2.61 eV） together with strong aromatic character of C₆₀F₁₈ and C₆₀Cl₃₀ indicate their high chemical stabilities. The electronic property investigations show that C₆₀F₁₈ and C₆₀Cl₃₀ could be excellent electron acceptors in consequence of their large vertical electron affinities. The density of states and frontier molecular orbitals present that the HOMOs and LUMOs for C₆₀F₁₈ and C₆₀Cl₃₀ are mainly distributed in the cage subunits, and the influence from halogen atoms is secondary. Enhancement of static linear polarizability and second-order hyperpolarizability of C₆₀F₁₈ and C₆₀Cl₃₀ further establishes them as potential candidates for nonlinear optical devices.5. The geometrical structures, thermochemistry, electronic and optical properties of C₅₆X₁₀ （X=H, F, and Cl） have been performed. The equatorial carbon atoms in C₅₆X₁₀ are saturated by X atoms and change to sp³ hybridization to release the large local strains. The addition reaction C₅₆+5X₂â†'C₅₆X₁₀ are highly exothermic, together with large energy gaps （ from 2.84 to 3.00 eV）, indicating their high chemical stabilities. The density of states is also calculated, which suggest that the frontier molecular orbitals of C₅₆X₁₀ are mainly from the carbon orbitals of two separate annulene subunits, and the contributions deriving from X atoms are relative smaller. In addition, the ultraviolet-visible spectra and second-order hyperpolarizabilities of C₅₆X₁₀ predicted that the second-order hyperpolarizabilities are larger than those of C₆₀ due to lower symmetric structures and high delocalization ofÏ€electron density on the two separate annulene subunits.