Recent Developments in Kramers’ Theory of Reaction Rates

• Published in: Chemphyschem 2023-08, Vol.24 (16), p.e202300272-n/a
• Main Authors: Pollak, Eli, Miret‐Artés, Salvador
• Format: Article
• Language: English
• Subjects: Chemical reactions; Diffusion rate; Friction reduction; Kramers turnover theory; Levitation; Nanoparticles; Polaritons; quantum tunneling and reflection; Surface diffusion; transition state theory
• ISSN: 1439-4235; 1439-7641
• DOI: 10.1002/cphc.202300272

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. Illustration of Kramers’ turnover theory for surface diffusion. Escape rate is plotted as a function of the scaled friction for a cosine potential simulating the one‐dimensional motion of Na atoms on a Cu(001) lattice at surface temperature T=110 K.