We present quantum chemical molecular dynamics (MD) simulations for a model formation process of fullerene molecules. Trajectories of up to 24-ps lengths were computed for (5,5), (7,3), (8,0), (9,0), (10,0), and (10,5) open-ended single-walled carbon nanotubes for a temperature range between 2000 and 4000 K at various tube lengths, using density functional based tight-binding (DFTB) molecular dynamics. DFTB was selected because geometries and energies obtained are found to qualitatively agree with B3LYP/6-31G(d) results at much smaller cost of computer time. Extremely fast cage formation was observed with simulation times as short as 3 ps, and most simulations at 3000 and 4000 K led to the formation of fullerene structures within less than 14-ps simulation times. Key structural features for the transformation of tubes to fullerenes are identified, such as the overwhelming presence of acetylenic “wobbling C2 units”, which form spontaneously in great abundance at the open ends of the tubes. A comparison of ...