We have employed the generalized energy-based fragmentation (GEBF) approach to investigate the structures, energies, and enthalpies of alpha-helices, 3(10)-helices, and beta-strands for capped polyalanines, acetyl(ala)(N)NH2, with N values from 8 to 40 at several theoretical levels. The M06-2X functional is demonstrated to be much more accurate than the B3LYP functional for peptides under study. On the basis of the GEBF-M06-2X results, we find that alpha-helices are more stable than the corresponding 3(10)-helices for all peptides with N >= 10. The cooperative interaction in both helices have not reached their asymptotic limits even for N = 40. By comparing the performance of the M06-2X, B3LYP, and the van der Waals corrected B3LYP, we show that both electrostatic and van der Waals interactions are essential for describing the cooperative interaction in long helices. In addition, the greater cooperativity of alpha-helices over 3(10)-helices in long helices is found to originate mainly from the much stronger van der Waals interaction in alpha-helices.