Assessment of hydrophobic interactions and their contributions through the analysis of the methane dimer

Hydrophobic Interactions (HIs) are important in many phenomena of molecular recognition in chemistry and biology. Still, the relevance of HIs is sometimes difficult to evaluate particularly in large systems and intramolecular interactions. We put forward a method to estimate the magnitude and the different contributions of a given HI of the C···C, H-C···H, and H···H type through (i) the analysis of the electron density in the intermolecular region for eleven relative orientations of the methane dimer and (ii) the subsequent decomposition of the corresponding interaction energy in physically significant contributions using Symmetry Adapted Perturbation Theory (SAPT). Strong correlations were found between the topological properties of ρ(r) calculated at intermolecular bond critical points and Eint(SAPT) plus its different contributions with the C···C distance of the considered orientations of (CH4 )2 . These correlations were used to construct Mollier-like diagrams of Eint(SAPT) and its components as a function of the separation between two carbons and the orientation of the groups bonded to these atoms. The ethane dimer and tert-butylcyclohexane are used as representative examples of this new approach. Overall, we anticipate that this new method might prove useful in the study of both intramolecular and intermolecular HIs particularly of those within large systems wherein SAPT or electronic structure calculations are computationally expensive or even prohibitive.