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Study about properties of fullerenes with medicinal and electronic applications have been made the highly useful and effective results for applications in different areas of science. Since the discovery of fullerenes (C n ), one of the main classes of carbon compounds, the unusual structures and physiochemical properties of these molecules have been discovered, and many potential applications and physicochemical properties have been introduced. Up to now, various empty carbon fullerenes with different numbers "n" had been obtained. The linear uniform field electric dipole polarizability tensors of fullerenes in the range C 20 through C 240 were calculated by the Olson Sundberg atom monopole-dipole interaction (AMDI) theory, Zhang et al. and Shanker and Applequist studies using the monopole and dipole polarizabilities of the carbon atom found previously to fit polarizability tensors of aromatic hydrocarbons. Topological indices are digital values that are assigned based on chemical composition. These values are purported to correlate chemical structures with various chemical and physical properties. They have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, were extended the calculation of the parameters concern to atom monopole-dipole moment such as AMDI (in Å 3 , Atom monopole-dipole interaction theory; α 1 to α 3 and α), Ellipsoid (in Å 3 , α 1 to α 3 and α) and semi-axes a,b,c of a thin ellipsoidal shell of uniform thickness (in Å, abc α 1 to α 3 ) for C 20 through C 300 .

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