Surface diffusion coefficients: Substrate dynamics matters

The pre-exponential factors for Cu adatom diffusion on Cu(001), (110), and (111) are examined within the framework of the harmonic transition-state theory and the embedded-atom method in order to precisely assess the role of the substrate dynamics. We find that the substrate cannot be ignored for an accurate determination of the prefactors: its contribution to the Helmholtz vibrational free energy is typically of the same order as that of the adatom and often of opposite sign so that significant cancellation may occur. These results provide a convenient pathway for the proper calculation of prefactors by using, e.g., ab initio methods.