Crossover between the adiabatic and nonadiabatic electron transfer limits in the Landau-Zener model

The semiclassical models of nonadiabatic transition were proposed first by Landau and Zener in 1932, and have been widely used in the study of electron transfer (ET); however, experimental demonstration of the Landau-Zener formula remains challenging to observe. Herein, employing the Hush-Marcus theory, thermal ET in mixed-valence complexes {[Mo₂]-(ph)_n-[Mo₂]}⁺ (n = 1-3) has been investigated, spanning the nonadiabatic throughout the adiabatic limit, by analysis of the intervalence transition absorbances. 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 (κ_el) of ∼0.5, which is contributed by the single and the first multiple passage. This study shows that in the intermediate regime, the ET kinetic results derived from the adiabatic and nonadiabatic formalisms are nearly identical, in accordance with the Landau-Zener model. The obtained insights help to understand and control the ET processes in biological and chemical systems.