Geometric, electronic, and vibrational structures of ${\mathrm{C}}_{50}$, ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, and ${\mathrm{C}}_{80}$

We have performed a molecular-dynamics simulation combined with the empirical tight-binding total-energy calculation method to study the carbon clusters ${\mathrm{C}}_{50}$, ${\mathrm{C}}_{60}$, ${\mathrm{C}}_{70}$, and ${\mathrm{C}}_{80}$. The optimized structure of ${\mathrm{C}}_{60}$, obtained by slow quenching from finite-temperature molecular dynamics, gives excellent agreement with results reported previously. The corresponding cluster structures are also determined through this calculational scheme. A systematic study of the geometric, electronic, and vibrational properties of these clusters is carried out and compared with other results.