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First-principles DFT (B3LYP) levels of calculations with the basis set 3-21G have been carried out in order to study the geometric stability and electronic properties of hydrogen passivated graphene (H-graphene) clusters(CN) (where N = 6, 10, 13, 16, 22, 24, 27, 30, 35, 37, 40, 42, 45, 47, 48, 50, 52, 54, 70 and 96) and perform the DOS spectrum on H-graphene (C16H10, C24H12, C30H14, C48H18, C70H22 and C96H24) using Mulliken population analysis by the Gaussian 03 W set of programs. The variations of ground state energy of graphene clusters are observed on sizes and corresponding number of carbon atoms. The binding energy per carbon atom is the function of carbon atoms for the number of carbon atoms less than 30 and saturated at carbon’s number 30 and more in the DFT (B3LYP) levels of approximation with the basis set 3-21G. The binding energy per carbon atom of a pure graphene sheet C32 is 8.03 eV/atom in the DFT (B3LYP) level of approximation with the choice of the basis set 3-21G, which is acceptable with previous reported data 7.91 eV/atom. The HOMO-LUMO gap in NBO is studied for some H-grapheneclustors C16H10, C24H12, C30H14, C48H18, C70H22 and C96H24.

The Hydrogen Passivated Graphene Cluster and its Stability - First Principle DFT (B3LYP) Levels of Approximation with the Basis Set 3-21G