Development and Applications: Complex hydrogen bonding networks in liquids and solutions
Hydrogen bond networks, graph theory, Ricci curvature, Forman-Ricci, and Ollivier-Ricci.
Over the last two decades, network science has experienced surprising growth. This is due to its capacity, versatility, and applicability in the study of complex systems. Network science has sought distinct patterns and behaviors, mainly through topological characteristics. In this context, analyses have been expanded and consolidated through tools inspired by geometry, such as Ricci curvature discretizations. In this work, the Ollivier-Ricci and Forman-Ricci curvatures are applied to hydrogen bond networks obtained from simulations for three situations: bulk water at atmospheric pressure and different temperatures; mixtures composed of water and methanol; and water confined in reverse micelles. Network curvature analysis proved to be a promising tool, since changes in the mean curvature values and in the shape of the distributions could be observed. The effectiveness of the Forman-Ricci curvature can also be verified, since, even requiring less computational demand, it showed results similar to those of the Ollivier-Ricci curvatures.