Theoretical Study Of The Non-classical Fullerenes With Heptagon(s) And Their Hydrides

In this paper, density functional theory (DFT) calculations were performed on non-classical C32H32-C36H36 with heptagons and non-classical fullerenes C46-C54 to put insight into the relationship between their structures and stability.The following three parts are included in the paper:1. A systematic study was performed on C32H32, C34H34 and C36H36 at the Hartree-Fock and density functional theory levels of theory. The calculated results demonstrate that the lowest-energy isomer is classic for C32H32 and non-classic for C34H34 and C36H36. For C32H32 and C34H34, the pentagon-pentagon fusions are an important factor in determining their stability. For C36H36 the lowest-energy isomers containing heptagons are all more stable than the corresponding one of classic structures and the pentagon-pentagon fusions determine their stability. Our calculations reveal that fullerene derivatives may not only violate the isolated pentagon rule but also may be non-classic structures containing'heptagon(s).2. Density functional theory calculations are performed on nonclassical fullerenes Cn (n=46,48,50 and 52) to give insight into their structures and stability. The calculated results demonstrate that the classical isomers generally satisfy the pentagon adjacency penalty rule. However, the nonclassical isomers with a heptagon are more energetically favorable than the classical ones with the same number of pentagon-pentagon bonds (B55 bonds), and many of them are even more stable than some classical isomers with fewer B55 bonds. The nonclassical isomers with the lowest energy are higher in energy than the classical ones with the lowest energy, since they have more B55 bonds. Generally, the HOMO-LUMO gaps of the former are larger than those of the latter. The sphericity and asphericity are unable to rationalize the unique stability of the nonclassical fullerenes with a heptagon. The pyramidization angles of the vertices shared by two pentagons and one heptagon are smaller than those of the vertices shared by two pentagons and one hexagon. It is concluded that the strain in the fused pentagons can be released by the adjacent heptagons partly, and consequently, it is a common phenomenon for nonclassical fullerenes to violate the pentagon adjacent penalty rule.3. Density functional theory calculations demonstrate that non-classical isomers of fullerene C54 with one or two squares have unusual large HOMO-LUMO gaps; and those with a heptagon are more advantageous than the classical ones with the same number of B55 bonds, some of which are even more advantageous than some classical isomers with fewer B55 bonds. Geometrical analysis demonstrates that an embedded square lead to higher pyramidization angles and a heptagon however lower the pyramidization angles of the related vertexes. These findings suggest that a square may lead to additional strain; and heptagon may release the strain in fused pentagons.