An ab initio molecular orbital study of through-bond (TB) orbital interactions has been carried out on several series of diene hydrocarbons, 2(n)-17(n), in which the double bonds are covalently attached to a variety of rigid saturated hydrocarbon bridges with lengths, n, ranging from four to 17 C-C sigma bonds. The resulting TB pi(+),pi(-) and pi(+)*,pi(-)* splitting energies, Delta E(pi) and Delta E(pi*), respectively, were obtained at the HF/3-21G level of theory. The distance dependence of Delta E(pi) and Delta E(pi*) for each type of diene was fitted to the respective exponential decay profiles, Delta E(pi) = A exp(-beta(h)n) and Delta E(pi*) = B exp(-beta(e)n). It was found that both beta(h) and beta(e) were dependent on the nature of the hydrocarbon bridge. For example, beta(h) is found to range from 0.6 per bond for 3(n) to only 0.05 per bond for 7(n) and 8(n). The beta(h) values for the polynorbornane bridge dienes, 2(n), and the hybrid norbornane-bicyclo[2.2.0]hexane bridge dienes, 3(n), are notably larger than that for the divinylalkanes, 4(n), and Natural Bond Orbital (NBO) analyses revealed this to be due to destructive interference effects between the two main relays of the bridges in 2(n) and 3(n). A simple intuitive model, based on the parity rule of TB coupling, was developed to explore interrelay interference effects in TB coupling along various saturated hydrocarbon bridges. The parity rule model was successfully used to design systems 5(n)-16(n) in which the TB coupling between the two double bonds is greatly-enhanced by constructive interrelay interference. For example, the absolute value for Delta E(pi) for the 15-bond diene 8(15) is 0.21 eV, an extraordinarily large quantity, considering that the double bonds are 17 Angstrom apart, and beta(h) for the series 8(n) is only 0.05 per bond. TB coupling in the "superbridges" 7(n), 8(n), 11(n), 12(n), 15(n), and 16(n) can be up to two orders of magnitude stronger than that present in 2(n) and 3(n). The enhanced degree of TB coupling in the former systems translates into a predicted increase in the rate of hole transfer in the cation radicals of 7(14) and 8(15) of four orders of magnitude, compared to that for the cation radical of 3(14). NBO analyses of TB coupling in 5(n) and 9(n) revealed that strong interrelay interference may occur even when one of the relays is not electronically coupled to either double bond. It was found that the original version of the parity rule required modification so that it takes into account any change in parity of a coupling pathway caused by sign inversions between coupling orbitals. A relative parity rule of TB coupling is proposed which correctly addresses the topology of orbital overlap. Compared to pi-TB coupling, TB interactions involving pi* orbitals are less affected by interrelay interference, constructive or destructive.