Recent Developments in Kramers’ Theory of Reaction Rates

Abstract

In this short review, we provide an update of recent developments in Kramers’ theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers’ theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.

Single-molecular diffusivity and long jumps of large organic molecules: CoPc on Ag(100)

“…As such, long jumps replace a single jump in the atomistic picture and while the total number of jumps follows an exponential increase with temperature, the occurrence of particular jump types does not. For single atom diffusion, long jumps become clearly more important as the temperature increases ( Braun and Ferrando, 2002 ; Pollak and Miret-Artés, 2023 ) and it has also been suggested that these are a general feature of hydrogen diffusion on close-packed transition metal surfaces at high temperatures ( Townsend and Avidor, 2019 ).…”

Statistical Mechanics Approaches for Studying Temperature and Rate Effects in Multistable Systems

“…As a matter of fact, when we study the out-of-equilibrium dynamics, the representation based on the sequence of basins and spin discrete variables is not sufficient since the relaxation times of the system depend on the energy barriers between the potential wells [61,98]. This is consistent, e.g., with the Kramers rate formula, originally formulated to deal with chemical reaction rates [99][100][101][102][103]. The consideration of the possible rate effects is particularly important when the stretching of the macromolecular chains, or other nanosystems, is performed with a large traction velocity [104,105].…”