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The theory given here shows how certain of the virtual orbitals of self-consistent field (SCF) theory provide a natural ingredient for constructing basis functions to study the shape resonances associated with temporary molecular ions. We give specific calculations of resonant behavior in H2, N2, ethylene, cyclopropene, and cyclobutene. In addition, we show how the theory can rationalize the relationship between Koopmans' theorem values of the energy of a resonance and the experimental values. The Journal of Chemical Physics is copyrighted by The American Institute of Physics.