Quantification of Reaction Barriers under Diffusion Controlled Conditions

In quantum chemistry, diffusion-controlled reactions are typically characterised by a monotonous rise in 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. While standard quantum chemical models fall short in capturing this phenomenon, we have developed a cost-efficient method to address this challenge. By tracking changes in covalent bonding based on quantum chemical descriptors, we can model the onset of entropy along the reaction path, by defining a cutoff which indicates the halfway point in the entropy gain. Utilizing a sigmoid fit function to model the entropy change, we obtain a a transition state in the free energy surface for such reactions. Our methodology is robust and suitable for diverse complexes within both organic and inorganic chemistry.