This work presents a new kind of odd–even effect involving an adsorbed impurity in methylenic bridges with an even number of carbons that causes a deviation in the Simmons model. The systems studied are composed of an extended molecule containing an even number of carbons forming a dopped methylenic bridge with an impurity, attached to two gold clusters. Changing the sites of an acceptor impurity (NO2) in the even methylenic bridges containing M carbon atoms (M = 8, 10, 12, and 14), an oscillating behavior of the energies' gap between HOMO/HOMO-1 and LUMO/LUMO + 1 molecular orbitals was observed. The gaps oscillate as a function of the site's parity where the impurity was adsorbed and can be explained by considering multiple avoided-crossing phenomena. The results show a strong dependence of the electrical conductance as a function of the adsorbed site with a deviation of the Simmons model due to the impurity.