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Semiclassical instanton theory is a form of quantum transition-state theorywhich can be applied to computing thermal reaction rates for complex molecularsystems including quantum tunneling effects. There have been a number ofattempts to extend the theory to treat microcanonical rates. However, theprevious formulations are either computationally unfeasible for large systemsdue to an explicit sum over states or they involve extra approximations whichmake them less reliable. We propose a robust and practical microcanonicalformulation called density-of-states instanton theory, which avoids the sumover states altogether. In line with the semiclassical approximations inherentto the instanton approach, we employ the stationary-phase approximation to theinverse Laplace transform to obtain the densities of states. This can beevaluated using only post-processing of the data available from a small set ofinstanton calculations, such that our approach remains computationallyefficient. We show that the new formulation predicts results that agree wellwith quantum scattering theory for an atom-diatom reaction and with experimentsfor a photoexcited unimolecular hydrogen transfer in a Criegee intermediate.When the thermal rate is evaluated from a Boltzmann average over our newmicrocanonical formalism, it can overcome some problems of conventionalinstanton theory. In particular, it predicts a smooth transition at thecrossover temperature and is able to describe bimolecular reactions withpre-reactive complexes such as CH3OH + OH.

Microcanonical Tunneling Rates from Density-of-States Instanton Theory