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By Edwin Bidwell Wilson

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Nat Nano,3,6, (356-362),1748-3387 Ju, S. , W. P. Kopcha, et al. (2009). Brightly Fluorescent Single-Walled Carbon Nanotubes via an Oxygen-Excluding Surfactant Organization. Science,323,5919,(Mar) (13191323),0036-8075 Ju, S. Y. and F. Papadimitrakopoulos (2008). Synthesis and redox behavior of flavin mononucleotide-functionalized single-walled carbon nanotubes. Journal of the American Chemical Society,130,2,(Jan) (655-664),0002-7863 Kania, P. and P. Oelhafen (1995). Photoluminescence study of <100> textured CVD diamonds.

Graphene segregated on Ni surfaces and transferred to insulators. , S. C. Bayliss, et al. (1996). The stable blue and unstable UV photoluminescence from carbon nanoclusters embedded in SiO2 matrices. Solid State Communications,99,12, (883-886),0038-1098 Zhang, R. , E. Bertran, et al. (1998). Size dependence of energy gaps in small carbon clusters: the origin of broadband luminescence. Diamond and Related Materials,7,1112, (1663-1668),0925-9635 Zhang, R. , T. S. Chu, et al. (2000). A Theoretical Study on the Interactions of Hydrogen Species with Various Carbon and Boron Nitride Phases.

9) i,j The term Ui,j describes the Coulomb repulsion Ui,j = e2 4π 0 | Ri − R j | (10) between two electrons on different sites (Ri = R j ). The on-site repulsion was chosen to Uii = 15eV. We solve the Hamiltonian H + HC within the Hartree approximation, wherein the many-body electron-electron interaction (9) is replaced by the electrostatic potential from charge distribution in the system. Hence, we replace (9) by the Hartree Hamiltonian HH = N ∑ Vi ni (11) i with Vi = N ∑ Ui,j j nj . (12) 40 Physics and Applications of Graphene - Theory The problem is solved self-consistently; after the initial determination of an eigensystem from Hamiltonian (6), the Coulomb part (11) is calculated and the eigensystem updated; this procedure is repeated until a converged solution is obtained.

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