Energetics of the Basic Allotropes of Carbon

An effort was made in this work to calculate the total ground state energy and electronic band structure of Fullerenes (C60), Graphite and Diamond using FHI-aims Density Functional Theory (DFT) code. The density functionals used are the local-density approximation (LDA) in the parameterization by Perdew and Wang 1992, Perdew and Zunger 1981, the generalized gradient functional PBE, and PBE+vdW approach as defined by Tkatchenko and Scheffler. The results obtained from the computations of the ground state energies of diamond, fullerenes and graphite were -2072.569 eV, -1027.178 eV and -2070.938 eV respectively. These results agree well when compared to the various exchange and correlation functionals used in this study. Similarly, the results obtained from the computations of the Kohn Sham electronic band gaps of graphite and diamond were 0.00072 eV and 5.57611 eV, respectively. These are also in agreement when compared to the experimental values of 0eV and 5.5eV. These band gaps are within reasonable overestimation errors of 0.0007 eV and 0.08 eV respectively. However, fullerenes band gap of 8.21131eV is not in agreement with the theoretical and experimental values of 1.83eV and 2.3eV, respectively. This is probably due to the Bucky-ball nature of Fullerenes as well as the lattice constants and physical settings used.