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

By the example of several typical thermally activated processes in atomic clusters, organic molecules, and nanostructures, it is shown that calculations of the corresponding pre-exponential factors in the Arrhenius law according to the Vineyard formula are in good agreement with the molecular dynamics simulation data for temperature dependences of characteristic times of these processes. This "static" approach (together with the determination of the activation energy through the examination of the potential energy hypersurface) provides information on kinetic characteristics of the system without resorting to numerical simulation of the time evolution, which requires large computer resources.