Calculation of the probability for ionic association and dissociation reactions by molecular dynamics and umbrella sampling

Investigating chemical reactions by computational techniques and finding new ways to study these reactions is an important necessity in the fields of chemistry, chemical engineering and biology. In this study, we have presented a new procedure for studying the interactions between divalent metal ions and carboxylates by using umbrella sampling. In some cases, it is more convenient to use variable coordinate reaction probabilities instead of potential energy or free energy curves, which in general are more widely used and available in the literature. Particularly, for practical purposes in building multi-scale models it could be more convenient to use the probability of reaction as a function of the separation distance between two carboxylate moieties when they are simultaneously associated to a metal ion. In this work, we have modelled the interactions between two carboxylates (propanoate ions) and divalent metal ions (calcium or magnesium) in order to obtain the probability of reaction as a function of the separation distance between the two carboxylates. By calculating the probability, it also became apparent that in the system containing calcium, the carboxylates have higher probability of reaction compared to the system containing magnesium. Furthermore, the presented probability could be also used for other multi-scale modelling purposes where these interactions are of main importance. The proposed procedure could also have application in other systems of interest.