In order to understand the very different rates of beta-scission reactions in cubylcarbinyl (1) and homocubyl (3) radicals, ab initio calculations have been performed on these and other polycyclic radicals in which the scissile bond is part of a four-membered ring. The finding of a Bell-Evans-Polanyi relationship between the calculated values of Delta H and E(a) for the beta-cleavage reactions of 1, 3, bicyclo[2.2.0]hexylcarbinyl (7), bicyclo[1.1.1]pentylcarbinyl (9), and basketyl (11) radicals with r(2) = 0.997 indicates that the rates of these reactions parallel their exothermicities. However, this parallel is not found in the beta-scission reaction of either 1-bicyclo[1.1.1]pentyl (13) or 2-bicyclo[1.1.1]pentyl (15) radicals. Despite the high exothermicities calculated for both reactions, the activation energies are also computed to be very high. Population analyses support the hypothesis that the transition states for beta-cleavage in 13 and 15 are destabilized by strong antibonding interactions between the two AOs to which the SOMO is largely confined. Comparison of the transition state geometries calculated for the eight beta-scission reactions studied indicates that only the transition states for beta-cleavage in 13 and 15 are substantially destabilized by overlap between the AOs of the SOMO.