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By the example of several typical thermally activated processes in atomicclusters, organic molecules, and nanostructures, it is shown that calculationsof the corresponding pre-exponential factors in the Arrhenius law according tothe Vineyard formula are in good agreement with the molecular dynamicssimulation data for temperature dependences of characteristic times of theseprocesses. This "static" approach (together with the determination of theactivation energy through the examination of the potential energy hypersurface)provides information on kinetic characteristics of the system without resortingto numerical simulation of the time evolution, which requires large computerresources.

On the Vineyard Formula for the Pre-Exponential Factor in the Arrhenius Law