Since the discovery three decades ago, fullerenes as well as metallofullerenes have been extensively investigated. However, almost all known fullerenes follow the classical definition, that is, classic fullerenes are comprised of only pentagons and hexagons. Nowadays, more and more evidence, from both theoretical and experimental studies, suggests that non-classical fullerenes, especially heptagon-containing fullerenes, are important as intermediates in fullerene formation mechanisms. To obtain fundamental understandings of fullerenes and their formation mechanisms, new systematic studies should be undertaken. Although necessary tools, such as isomer generating programs, have been developed for classical fullerenes, none of them are able to solve problems related to non-classical fullerenes. In this thesis, existing theories and algorithms of classical fullerenes are generalized to accommodate non-classical fullerenes. A new program based on these generalized principles is provided for generating non-classical isomers. Along with this program, other tools are also attached for accelerating future investigations of non-classical fullerenes. In addition, research to date is also reviewed. / Master of Science / The thesis describes the generation of heptagon-containing fullerene structures based on generalized spiral algorithm. Details of algorithms and designs are discussed. The thesis is helpful for people who are working on fullerene geometry studies. The algorithms and programs provided by this thesis could be a good start for other investigations. For those who are not familiar with programming, the program provided by this thesis can also be used to generate and analyze heptagon-containing structures. In addition, this thesis can also be helpful for people working on areas that geometry analyses of molecules are necessary.

A family of novel large cage Tb-based TNT-EMFs Tb₃N@C_2n (40 ≤ n ≤ 44), and a family of novel dimetallic endohedral metalloazafullerenes with the molecular formula of M₂@C₇₉N (M=Y, Tb, and La), were for the first time systematically synthesized, isolated, and structurally characterized. The protocol developed in this thesis provides an effective and systematic method for the synthesis, purification, and characterization of TNT-EMFs and other novel EMFs. Structural information about this family of Tb-based TNT-EMFs strongly supports the TNT formation mechanism of TNT-EMFs. It also demonstrates for the first time that EMFs do not necessarily choose an IPR-obeying cage even if the IPR cages are available. At room temperature and in a non-polar organic solvent, the fluorescence of the hydrogenated product of Tb₃N@C₈₀ was for the first time successfully obtained based on the proposed idea: de-shielding the screen effect of the fullerene cage on the metal ions or clusters inside the fullerene cage. The structural characterization of Tb₂@C₇₉N using single crystal X-ray diffraction crystallography demonstrated that the fullerene cage of M₂@C₇₉N is an I_h eighty-atom cage. The presence of the N atom in the molecule was further confirmed by mass spectra of the ¹⁵N labeled samples. ESR data demonstrated that there is a single-electron bond between the two Y atoms in Y₂@C₇₉N molecules. Theoretical calculations showed for the first time that the single-electron bond is low-lying at the HOMO-2 orbital and thereby resulting in a large HOMO-LUMO gap. It is, in fact, this large HOMO-LUMO gap and the low-lying single-electron orbital (hidden at HOMO-2) that are jointly responsible for the stability of M2@C79N. The single-electron bonds are the longest metal-metal bond reported so far. The chromatographic retention behavior of TNT-EMFs was also systematically studied on 5PBB and 5PYE columns. Both experimental and theoretical data demonstrated that the 5PBB column is sensitive to a fullerene's predicted cage size but indifferent to its cage symmetry, while the 5PYE column is more sensitive to the density and distribution of Ï electrons in a fullerene cage. Therefore, the 5PYE column is more suitable for separating structural isomers. The combination of the 5PBB column in the first stage and the 5PYE column in the second provides a highly effective way for isolating specific isomers. / Ph. D.