This study extends the Binary Digit Memory (BDM) model and explores its application to CO₂ reduction catalysis. Originally developed to model memory induction through covalent modifications, the BDM model is a mathematical framework that describes switching dynamics in systems with multiple sites. We adapt this model for catalytic processes by coupling it with the Schrödinger equation to account for multi-electron dynamics on catalyst surfaces. The research is structured into three main chapters. Chapter 2: We perform a formal analysis of the BDM-ODE system using the mean-field approximation. This approach simplifies the high-dimensional system and reveals critical phenomena such as hysteresis and bifurcations, which are essential for understanding catalytic behavior. Chapter 3: We refine these findings using renormalization group (RG) theory, which rigorously justifies the mean-field approximation and uncovers the scaling universality of the system's critical behavior as the number of sites, N, increases. This universality ensures consistency in predictions across different scales. Chapter 4: We apply this framework to CO₂ reduction. We introduce a coupled system where the Schrödinger equation governs electron dynamics on the catalyst surface, while the BDM-ODE system manages the switching dynamics. Using the Hartree approximation and RG-validated mean-field methods, we simulate the CO₂ reduction process and optimize catalytic performance. Simulations demonstrate significant improvements in yield and efficiency. This interdisciplinary approach integrates nonlinear dynamics and quantum mechanics, offering new insights into CO₂ reduction catalysis. By leveraging the strengths of the BDM model and combining it with quantum mechanical principles, we establish a robust theoretical foundation for enhancing catalytic processes, with potential implications for sustainable energy solutions.
Isamu Ohnishi (Sun,) studied this question.