Topological descriptors and Laplace spectra in simple hydrogen bonded systems

Abstract

Topological descriptors related to the size distribution of hydrogen bonded clusters are scrutinized systematically, primarily from the point of view of their applicability for locating the percolation transition point. As a first step, we focus on regular, relatively simple systems like ice polymorphs (cubic, hexagonal, ice VI and ice VII), in order to monitor the evolution of these descriptors with varying the hydrogen bonding probability. Further quantities are also introduced, like the ratio of the number of molecules that do not belong to any ring structure, by which it is possible to determine a critical bonding probability below that the system shows dominantly chain-like behaviour. By means of calculating the smallest eigenvalues of the Laplace spectra of hydrogen bonded networks, yet another way has been developed for determining the percolation transition point. Results concerning the percolation transition agree well with those arising from more traditional ‘toolbox’ calculations. Finally, the aforementioned descriptors have been calculated for more realistic systems, with the aim of understanding better the properties of hydrogen bonded networks in important alcohol-water solutions.