B3LYP calculations with two different basis sets have been performed to understand why bicyclo[2.2.0]hex-1(4)-ene (1a) undergoes dimerization with Delta H double dagger = 11.5 kcal/mol, but dimerization of perfluorobicyclo-[2.2.0]hex-1(4)-ene (1b) has never been observed. The former reaction is computed to be exothermic by 37.2 kcal/mol, whereas the latter is calculated to be endothermic by 7.4 kcal/mol. The 44.6 kcal/mol difference between the enthalpies of these two reactions can be dissected into contributions of 24.5 kcal/mol for the difference between the enthalpies for forming diradical intermediates 2a and 2b and 20.1 kcal/mol for cyclization of 2a and 2b to, respectively, 3a and 3b. The latter enthalpy difference is largely attributable to repulsions between the endo-fluorines in the dimer, although the exo-fluorines also are found to contribute. The former enthalpy difference is attributable to the difference between the dissociation enthalpies of the pi bonds in 1a and 1b, which is shown to amount to 16 +/- 1 kcal/mol. About 25% of the stronger pi bond in fluoroalkene 1b is found to be due to hyperconjugation of the eight C-F bonds in 1b with the filled pi orbital. However, the major contributor to the stronger pi bond in 1b is shown to be the unfavorable interaction that results when a pyramidalized radical center is syn to a C-F bond. Both of these effects, which contribute to the greater strength of the pi bond in 1b, relative to that in 1a, are analyzed and discussed.