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

TL;DR

This study uses spectral clustering of the Laplace matrix to analyze the H-bonded network in liquid water, revealing consistent community structures and differences between surface and interior molecules.

Contribution

It introduces a spectral clustering approach based on Laplace spectra to characterize the global properties of water's hydrogen-bonded network.

Findings

Six communities are consistently formed regardless of system size.

Surface molecules have a higher fraction of four-coordinated molecules.

Periodic boundary conditions influence clustering behavior.

Abstract

Application of the spectral clustering method based on the analyses of the Laplace matrix is an acceptable indicator of the global properties of H-bonded network. 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. We showed that the H-bonded environment on the surface of the clusters is different from what can be found inside of the clusters. The fraction of four-coordinated molecules is significantly larger in the case of surface molecules. Our work emphasizes that the periodic boundary conditions always cause clustering in the system.