Quantification and origin of cooperativity: insights from density functional reactivity theory

Cooperativity is a widely used chemical concept whose existence is ubiquitous in chemical and biological systems but whose quantification is still controversial and origin much less appreciated. In this work, using the interaction energy of a molecular system, which is composed of multiple copies of a building block, we propose a quantitative measurement to evaluate the cooperativity effect. This quantification approach is then applied to six molecular systems, i.e., water cluster, argon cluster, protonated water cluster, zinc atom cluster, water cluster on top of a graphene sheet, and alpha helix of glycine amino acids, each with up to 20 copies of the building block. Cooperativity is seen in all these systems. Both positive and negative cooperativity effects are observed. Employing the two energy partition schemes in density functional theory and the information-theoretic quantities such as Shannon entropy, Fisher information, information gain, etc., we then examine the origin of the cooperativity effect for these systems. Strong linear correlations between the cooperativity measure and some of these theoretical quantities have been unveiled. With these correlations, we are able to quantitatively account for their origin of cooperativity. Our results show that the interactions governing the existence and validity of the cooperativity effect are complicated. An opposite mechanism in enthalpy-entropy compensation for positive and negative cooperativity has been unveiled. These results should provide new insights and understandings from a different viewpoint about the nature and origin of cooperativity to appreciate this vastly important chemical concept.