Quantification of Reaction Barriers Under Diffusion Controlled Conditions

In quantum chemistry, diffusion-controlled reactions are typically characterized by a monotonous rise in the electronic energy, indicative of a barrierless process. In reality, this change in electronic energy is accompanied by an increase in entropy, thereby introducing a barrier in free energy. Standard quantum-chemical models fall short in capturing this phenomenon, but we have developed a cost-efficient method to address this challenge. By tracking changes in bonding based on quantum chemical descriptors, we can model the onset of entropy along the reaction path by defining a cutoff that indicates the halfway point in the entropy gain. Utilizing a sigmoid fit function to model the entropy change, we obtain a transition state on the free energy surface for diffusion-controlled reactions. Our methodology is robust and suitable for diverse complexes within both organic and inorganic chemistry.