Comparison of geometric, electronic, and vibrational properties for isomers of small fullerenes C₂₀-C₃₆

We employ the self-consistent-charge density-functional tight-binding (SCC-DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C ₂₀, C₂₄, C₂₆, C₂₈, C₃₀, C₃₂, C₃₄, and C₃₆, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C₂₀-C ₁₈₀. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed.