Graphene can be viewed as sheet of benzene rings fused together forming a variety of structures including the trioxotriangulenes (TOTs) which is a class of organic molecules with electro-active properties. In order to clarify such properties, structures and electronic properties of the graphene fragments phenalenyl, triangulene, 6-oxophenalenoxyl, and X3TOT (X = H, F, Cl) are computed. Validation of the methodologies are carried out using the density functionals B3LYP, M06-2X, B2PLYP-D, and the MP2 theory, giving equilibrium geometries of benzene, naphthalene, and anthracene with mean unsigned error (MUE) of only 0.003, 0.007, 0.004, and 0.007 A, respectively in relation to experiment. (C) 2017 Elsevier B.V. All rights reserved.