The ability to control chemical reactions involving molecules attached to plasmonic nanoparticles requires information about vibrational energy flow. We compute the energy flow quantum mechanically in 5 substituted benzenethiols, including 4nitrobenzenethiol (NBT), attached to plasmonic nanoparticles as well as rates of energy transfer to the surroundings. The lifetimes computed for Raman-active modes match those measured experimentally and are found to mainly result from intramolecular vibrational energy redistribution. Variation in lifetimes among the molecules arises from the tuning of resonances via different chemical groups. The lifetime of the NO stretch of NBT, which when excited can facilitate reaction, is computed to be close to the measured value and depends largely on resonances involving 3 other modes. We find that, upon comparison with the results of recent picosecond time-resolved measurements, the plasmonic resonance transfers energy to an excited electronic state, followed by rapid internal conversion to the ground state and vibrational cooling.