Artificial resonance procedure for the determination of quantum mechanical rate constants in the tunneling regime

The quantum mechanical thermal rate constant associated with a bimolecular reactive collision is given by Miller [J. Chem. Phys. 61, 1823 (1974)] as the Boltzmann average of the reactive flux operator F 𝒫, F being the flux operator and 𝒫 a projection operator selecting reactants to products wave functions. We show with the help of the complex rotation method that at low enough temperatures, when tunneling is the dominant mechanism, this rate can also be obtained from a set of artificial resonances produced by box quantization. This device creates two wells, one in the reactant region, one in the product region and the resonances are associated with irreversible decay from one well to the other. Illustrative one-dimensional examples are given.