Electron transmission spectroscopy is used for determining the energies of vertical electron attachment to the empty pi* orbitals of ethene (1), 1,4-cyclohexadiene (2), 1,4,5,8-tetrahydronaphthalene (3), and 1,4,5,8,9,10-hexahydroanthracene (4), where the number of ethene double bonds, which interact through space and through the CH2 bridges, increases along the series. In contrast with the expectations based on a simple perturbational model, the energy of the first anion state is nearly constant on going from 1 to 4. Moreover, the energy splitting between the lowest and the highest anion states in the larger molecular systems 3 and 4 is smaller than in 1,4-cyclohexadiene. The experimental data are compared with the empty orbital energies of the neutral states supplied by HF calculations using both a standard basis set and one augmented with diffuse functions, using the exponent stabilization method for distinguishing the virtual orbitals which give rise to temporary anion states. The graphs of virtual orbital eigenvalues versus the exponent scaling factor display avoided crossings and regions where the pi(*) molecular orbital energies are relatively stable. The orbital energies determined in correspondence with the avoided crossings do not reproduce the trends of the resonances observed in the spectra. A better match with experiment (although not completely satisfactory) is obtained by determining the energies in the region of stability of the graphs. This set of results also predicts smaller through-space and through-bond interactions.