Accurate calculations of reaction rates: predictive theory based on a rigorous quantum transition state concept

In recent years the accurate and truly predictive calculation of thermal rate constants has become feasible for reactive systems consisting of more than only three or four atoms and results for benchmark six atom reactions as H + CH4 -> H-2 + CH3 were presented. The present article reviews research focusing on the accurate calculation of rates for reactions proceeding via barriers and highlights key method developments as well as important applications in the area. It discusses the quantum transition state concept which allows one to rigorously and efficiently compute averages with respect to thermal or micro-canonical ensembles and to interpret the results using intuitive pictures. Schemes for the construction of accurate high-dimensional potential energy surfaces required in quantum dynamics simulations and for performing efficient multi-dimensional wave packet dynamics calculations are also reviewed. As a result of the large number of accurate reaction rate calculations for diverse reactions which have been presented in about the last decade, a consistent picture of the importance of quantum effects in reaction rates emerged. The present article attempts to comprehensively describe this picture and in addition will try to provide guidelines when significant deviations for classical (harmonic) transition state theory can be excepted.