In materials and surface science, the prevalence of activated atomic-scale processes with barriers exceeding several k B T makes rare-event type dynamics more the norm than an exception. In corresponding systems, the dynamics is characterized by long residence times in a basin of the potential energy surface (PES), and infrequent crossings of PES transition states (TSs) to access another basin. The longer-term time evolution is then suitably described by a Markovian Master equation, which coarse-grains the continuous dynamics into discrete Markov jumps between the respective metastable system states and where the short-time dynamics within each basin is appropriately condensed into the rate constants k i j for individual jumps from state i to another state j. Rate theories thereby provide the link between the PES and the rate constant, within harmonic transition state theory (hTST) for instance k i j = ν i j exp(-∆E act i→ j /k B T ) with ν i j a vibrationalfrequency dependent prefactor and ∆E act i→ j the activation barrier connected with the TS.