Structural Relationship Between Degree of Unsaturation with Fermi Energy, Chemical Hardness, and The HOMO-LUMO Gap of (5,5) Armchair Single-Walled Carbon Nanotubes

Carbon nanostructure compounds in an attractive variation of structures and wonderful forms have been synthesized and identified. One of these structures is the carbon nanotubes. These structures have several rings that share number of carbons. Study about properties of nanotubes with medicinal and electronic applications have been made the highly useful and effective results for applications in different areas of science. One of the main recognized structures of nanotubes is (5,5) single-walled tube (SWCN). Topological indices are the digital value combined with chemical constitution purporting for correlation of chemical structures with various chemical and physical properties that have constructed the effective and useful mathematical methods for finding good relationship between several data of the properties in these materials. One of the useful numerical and structural items in unsaturated compounds is degree of unsaturation (DU ) which is illustrated here. In this study, the relationship between this index (DU ), Fermi energy (E f), chemical hardness, and relative energetic stability all show the length periodicity seen in the HOMO-LUMO gap, in contrast to the optical charge transfer transition are represented as some of the important properties of nanotubes (5,5) armchair SWCN. By the simple model presented here, in good approximation can calculate the structural and electronic properties of these nanotubes and can be used the approximated values in electronic structures and electrical properties studies of this type of nanotubes. The interesting results of relationship among DU and the properties of these nanotubes are presented.