The Study On Graphene's Structure With DFT And ABEEMσπ

In this article, we use Density Functional Theory(DFT) and the atom-bond electronegativity equalization method (ie. ABEEMσπmodel) to research graphene. Based on density functional theory and the electronegativity equalization principle, Professor Yang Zhongzhi and his team established the atom - bond electronegativity equalization (ABEEMσπ) model. In the model, the molecular system charge is divided into atomic charge and bond charge.This paper selects five configurations: complete single layer rectangle (41 carbon ring) graphene, complete single layer hexagonal (37 carbon ring) graphene, and contains one defect single layer defective rectangle (41 carbon ring) graphene, contains one defect single layer hexagonal (37 carbon ring) graphene, contains two defects of single layer rectangular graphene. All the configurations are optimized by B3LYP/6-31G (d, p) method.The main purpose of selects these five configurations is to study different graphene structure from the follow cases : (1) to compare the different configurations (hexagonal and rectangular) case. (2) to compare the same configuration with complete and defect case.(3) to compare the same configuration with one defect and two defects case.Statistics optimized configurations's bond length and bond angle,HOMO and LUMO,energy gap. We discovered that: (1) The values of the bond length and bond angle, are axisymmetric equivalent or centrosymmetric equivalent. (2) Different configurations, HOMO and LUMO distribution of different, energy gap values are also different. (3) The same configuration, the defect and pefect hexagonal graphene , HOMO and LUMO have different distribution, the former energy gap of about 0.9eV, with the conductor characteristics, the latter energy gap of 2.0 eV, is the nature of a semiconductor, and there are degenerate state.For rectangular graphene, the defective and complete configuration, HOMO and LUMO distribute in zigzag edges, the energy gap values are 0.15 eV, close to 0, with the nature of the conductor. (4) The rectangular configuration of graphene, with two defects and one defect, HOMO and LUMO does not change, mainly distributed in the zigzag edges. Energy gap is about t 0.15 eV. Analysis of the reasons, the edge is different, the zigzag edges's overlap ofπelectrons is more than the armchair-shaped edges, which impact on HOMO and LUMO and energy gap.As an armchair-shaped edges is different from zigzag edges, so in the ABEEMσπmodel, we defines the edge carbon atoms, the internal carbon atoms and theπbond on the carbon atoms, and then adjust the parameters, compared with the charge distribution which calculate by HF/STO-3G method, the linear correlation above 0.99. So the define of carbon atoms andπbond is reasonable, the adjusted parameters are suitable for macromolecular system of graphene.