Large positron annihilation cross sections have been observed for a variety of molecules at various energies below the threshold for positronium formation. These large values are due to vibrational Feshbach resonances ͑VFRs͒, in which the positron attaches to the molecule while exciting a vibration. This leads to rates of annihilation far greater than those expected for a simple collision. The dependence of the annihilation rate on incident positron energy can be used to deduce

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... binding energies. Presented here is a comprehensive study of resonant annihilation in small molecules ͑e.g., hydrocarbons with one or two carbon atoms͒. In some cases, only fundamental vibrations are important, and theory correctly predicts the annihilation rates as a function of incident positron energy. In other cases, combination and overtone vibrations are shown to support Feshbach resonances. In the subset of these cases where the positron-molecule coupling strengths can be determined for these combination modes, theoretical predictions are in agreement with the measurements. Finally, there are species that do not exhibit VFRs, such as carbon dioxide. This is interpreted as evidence that positrons bind very weakly or not at all to these targets. Several of these molecules exhibit a variety of behaviors that are presently unexplained. The implications of the results presented here for more comprehensive theories of positron annihilation on molecules are discussed.