The formal [2sigma + 2sigma + 2pi] cycloaddition of quadricyclane, 1, with dimethyl azodicarboxylate, 2, in water has been studied using DFT methods at the B3LYP/6-31G** and MPWB1K/6-31G** levels. In the gas phase, the reaction of 1 with 2 has a two-stage mechanism with a large polar character and an activation barrier of 23.2 kcal/mol. Inclusion of water through a combined discrete-continuum model changes the mechanism to a two-step model where the first nucleophilic attack of 1 to 2 is the rate-limiting step with an activation barrier of 14.7 kcal/mol. Analysis of the electronic structure of the transition state structures points out the large zwitterionic character of these species. A DFT analysis of the global electrophilicity and nucleophilicity of the reagents provides a sound explanation about the participation of 1 as a nucleophile in these cycloadditions. This behavior is reinforced by a further study of the reaction of 1 with 1,1-dicyanoethylene.