Coherent Spin Dynamics and the Magnesium-25 Isotope Effect in ATP Synthesis

This repository contains the original Python implementation of quantum mechanical simulations used to model the Magnesium Isotope Effect (MIE) in ATP synthase enzymatic centers. Unlike simplified kinetic models, this code employs the Haberkorn Master Equation approach to track the coherent spin evolution of [Mg-ADP ... Pi] radical pairs in 12-dimensional Hilbert space. The scripts reproduce key findings of our research: the transition from singlet-start suppression to triplet-start acceleration (Spin Blockade release) and the identification of the "kinetic window" where the isotope effect reaches its quantum resonance. The code is optimized for reproducibility and intended to support the manuscript submitted to The Journal of Physical Chemistry.