Mini Review on Revisiting Marcus Theory and Novel Understanding Heterogeneous Electron Transfer by Programing Tools

Electron transfer is always the spotlight in electrochemistry, especially electrochemical energy storage. However, the current understanding of electron transfer, particularly in heterogeneous systems as explained by Marcus theory, faces challenges in accurately accounting for surface effects, solvent reorganization, and quantum tunneling, which are critical to real-world applications. Here, this review presents a comprehensive analysis of the heterogeneous electron transfer processes within the framework of Marcus theory, focusing on computing approaches using Python and Wolfram Language. The introduction outlines the significance of Marcus theory in explaining electron transfer reactions and sets the stage for the subsequent discussions. In the results and discussions section, the electron distribution in heterogeneous systems is explored, comparing the effects of different formalisms on electron transfer. A detailed comparison of the computational approaches using Python and Mathematica underscores the essential role of programing in tackling complex electron transfer models. These tools offer powerful, complementary capabilities for simulating the nuanced behavior of heterogeneous electron transfer processes, providing researchers with the flexibility and precision necessary to address the limitations of traditional theoretical methods. Finally, the work delves into the law of conservation of energy within the context of Marcus theory, offering a nuanced discussion of its implications for electron transfer studies. This review aims to equip researchers with practical insights and computing tools to enhance their understanding and application of Marcus theory in heterogeneous systems.