The [3,3]-sigmatropic shifts of 1,5-hexadiyne, 1,2-hexadien-5-yne, 1,2,5-hexatriene, 1,2,4,5-hexatetraene, and 1-hexen-5-yne were studied, using a hierarchy of methods (RHF/6-31G*, MP2//RHF/6-31G*, BLYP/6-31G*, Becke3LYP/6-31G*, and CASSCF/6-31G*). Hartree-Fock, MP2, and density functional methods predict the mechanisms to be concerted, involving aromatic transition structures, whereas CASSCF/6-31G* favors the stepwise pathways via diradical intermediates. Both MP2//RHF/6-31G* and Becke3LYP/6-31G* give activation energies in good agreement with the experimental values. Becke3LYP is a reliable tool for predicting the activation energies of such reactions, although it has a tendency to overstabilize allene systems. The activation energies for the series of reactions are remarkably constant at 31-35 kcal/mol, consistent with the aromatic character of their transition states. The origin of this kinetic monotony even in the face of structural diversity is analyzed.