Molecular aggregation in liquid water: Laplace spectra and spectral clustering of H-bonded network

Abstract

Molecular dynamics simulations of pure ambient liquid water were performed. Hydrogen bond network properties were determined by calculation of eigenvectors and eigenvalues of the Laplace matrix. We investigated how these quantities depend on the system size, the coordination number and periodic boundary conditions taking into account different hydrogen bond definitions. It was found that the first peak of the Laplace spectra contains six eigenvalues. These results suggest that six communities are always formed in our simulated systems independently of the number of molecules in the cubic box. By the help of the spectral clustering method, which is an acceptable indicator of the global properties of H-bonded network, two different H-bonded environments were identified. The tetrahedrality of the water molecules is significantly larger at the surface than inside the clusters. This difference can be related to the coexistence of HDL and LDL domains in liquid water. Furthermore, our work also emphasizes that the periodic boundary conditions always cause clustering in the system.