Integrating Wolfram Language and Python into Marcus theory: computing toolbox and teaching for students

Abstract Marcus theory originally was proposed by scientist Rudolph A. In 1956, Marcus established a theoretical framework for elucidating the kinetics of outer-sphere electron transfer reactions. Further, Marcus theory experienced significant advancements from Marcus and other scientists, developing extensive applications across diverse fields, such as inorganic chemistry, analytical chemistry, materials chemistry, energy chemistry, life chemistry, photochemistry, and solution chemistry. Despite its significance, many chemistry students have challenges in comprehending the fundamental concepts of Marcus theory, particularly the physical interpretation of the associated equations. In this paper, we aim to help students understand well the basics of Marcus theory and improve their mastery of programming ability. It structures an integrated overview of Marcus theory, emphasizing its application through two formalisms on kinetic constant based on reorganization energy. One is a zero-order approximation, and the other one is a one-order approximation. Furthermore, novel modern computational methods are employed to visualize and elucidate the related equations and parameters of Marcus theory. The utilization of programming languages such as Wolfram Language and Python enables straightforward calculation demonstrations, minimizing the occurrence of errors or confusion while ensuring the permanent storage of the provided computing codes. We provide all the necessary codes for plotting and conducting comprehensive analyses, including a typical exercise used in the past 2 years. Our proposed methodology primarily targets graduate and undergraduate students with a certain foundation of chemical and computing knowledge. This work will highly enhance their good comprehension of Marcus theory and improve their valuable computational skills for future research. Graphical Abstract