Crossover between the Adiabatic and Nonadiabatic Limits of Thermal Electron Transfer: Verifying the Landau-Zener Formula

Abstract The semiclassical models of nonadiabatic transition were proposed first by Landau and Zener in 1932, which has been widely used in study of electron transfer (ET); however, experimental substantiation of the Landau-Zener formula remains challenging. Herein, employing the Marcus-Hush theory, thermal ET in mixed-valence complexes { [Mo2]-(ph)n-[Mo2] }+ (n = 1-3) is investigated and the Landau-Zener analysis performed in the adiabatic and nonadiabatic limits. Evidently, the Landau-Zener formula is valid in the adiabatic regime in a broader range of conditions than the theoretical limitation known as the narrow avoided-crossing. The intermediate system is identified with an overall transition probability (𝛋el) of ~ 0.5, which is resolved by the contributions from the single and the first multiple passage. The results unify the contemporary ET theories under the semiclassical framework. The obtained insights help to understand and control the ET processes in biological and chemical systems.