Topology Analysis For Infinite Single-walled Carbon Nanotubes

Bloch wave function which describes wave in the crystal is characterized by a plane wave function multiplying a periodic function. In dealing with the interactions of atoms, plane-wave quantum chemistry calculating softwaves use plane wave functions, while localized-wave quantum chemistry calculating softwaves use localized wave functions. Therefore, using localized wave functions to handle the crystal must be different from plane wave functions. Localized-wave quantum chemistry calculating softwaves extend user-defined primary cell or supercell to a very large molecules to get whole wave functions, however, it only outputs atomic orbital wave functions in user-defined area. Outputing wave function can not reproduce Bloch wave functions, but we can reproduce Bloch wave functions in a specific area. This paper uses (3,3) armchair singled-walled carbon nanotube as a research object to propose our method about using localized-wave quantum chemistry calculating softwaves to reproduce Bloch wave functions in the crystal.The carbon nanotube is a tubular structure, which has large length-to-diameter ratio and specific surface area. So it has many special properties compared with other materials and gets all scientists eyes. After twenty year since it was found, we get that macroscopic physical properties of single-walled carbon nanotubes are closed relationship with diameters. To get the nature of these relationship, we need to start analysis in the view of electronic structure.In this paper, density functional theory with hybrid B3LYP functional at6-31G*basis set level was used to get the electronic wave functions of single-walled carbon nanotubes, and then use the quantum theory of atoms in molecules (QTAIM) to analyze the electronic structure of single-walled carbon nanotubes. Research works are carried out sequentially in the following order:(a) research the effect of analyzing supercell region on properties for the crystal.Use density functional theory to obtarin the electronic wave functions for (3,3) single-walled carbon nanotube’s supercell with ten cells. Observe that properties have large deviation near the border of supercell, which is caused by the absence of wave functions. In the middle region, properties are stable, because the absence of wave functions are outside the direct distance. Also for this region, there is a slight difference for different carbon bonds. When using localized-wave quantum chemistry calculating softwaves to simulate crystal, the effect of missing wave functions needs to be study to find the region which is least affected. This region is generally in the middle of supercell.(b) research the effect of cell’s number on properties for the crystal.Also using density functional theory to obtarin the electronic wave functions for (3,3) single-walled carbon nanotube’s supercell with the number of primary cell changing from two to twenty, and then study the changes of properties’changing in the middle regions. For (3,3) single-walled carbon nanotubes, supercell with eight primary cells can get adequate precision. In addition, with the primary cell number increasing, the properties’changing in the middle supercell appears damping oscillation. This phenomenon can link the macroscopic and the microscopic and is the highlight of this paper.(c) research diameters’effect on properties for single-walled carbon nanotubes.Using density functional theory to study armchair and zigzag singled-walled carbon nanotubes’properties with diamters. We found that most electronic properties have linear correlation with the reciprocal of the square of diamters. Electronic properties have close contacted with each other and can be linked them together through diameters to show a clear image of electronic topolgy with diamters.