Issue 36, 2013

Hydrogen bond network topology in liquid water and methanol: a graph theory approach

Abstract

Networks are increasingly recognized as important building blocks of various systems in nature and society. Water is known to possess an extended hydrogen bond network, in which the individual bonds are broken in the sub-picosecond range and still the network structure remains intact. We investigated and compared the topological properties of liquid water and methanol at various temperatures using concepts derived within the framework of graph and network theory (neighbour number and cycle size distribution, the distribution of local cyclic and local bonding coefficients, Laplacian spectra of the network, inverse participation ratio distribution of the eigenvalues and average localization distribution of a node) and compared them to small world and Erdős–Rényi random networks. Various characteristic properties (e.g. the local cyclic and bonding coefficients) of the network in liquid water could be reproduced by small world and/or Erdős–Rényi networks, but the ring size distribution of water is unique and none of the studied graph models could describe it. Using the inverse participation ratio of the Laplacian eigenvectors we characterized the network inhomogeneities found in water and showed that similar phenomena can be observed in Erdős–Rényi and small world graphs. We demonstrated that the topological properties of the hydrogen bond network found in liquid water systematically change with the temperature and that increasing temperature leads to a broader ring size distribution. We applied the studied topological indices to the network of water molecules with four hydrogen bonds, and showed that at low temperature (250 K) these molecules form a percolated or nearly-percolated network, while at ambient or high temperatures only small clusters of four-hydrogen bonded water molecules exist.

Graphical abstract: Hydrogen bond network topology in liquid water and methanol: a graph theory approach

Supplementary files

Article information

Article type
Paper
Submitted
30 May 2013
Accepted
09 Jul 2013
First published
08 Aug 2013
This article is Open Access
Creative Commons BY-NC license

Phys. Chem. Chem. Phys., 2013,15, 15163-15171

Hydrogen bond network topology in liquid water and methanol: a graph theory approach

I. Bakó, Á. Bencsura, K. Hermannson, S. Bálint, T. Grósz, V. Chihaia and J. Oláh, Phys. Chem. Chem. Phys., 2013, 15, 15163 DOI: 10.1039/C3CP52271G

This article is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported Licence. You can use material from this article in other publications, without requesting further permission from the RSC, provided that the correct acknowledgement is given and it is not used for commercial purposes.

To request permission to reproduce material from this article in a commercial publication, please go to the Copyright Clearance Center request page.

If you are an author contributing to an RSC publication, you do not need to request permission provided correct acknowledgement is given.

If you are the author of this article, you do not need to request permission to reproduce figures and diagrams provided correct acknowledgement is given. If you want to reproduce the whole article in a third-party commercial publication (excluding your thesis/dissertation for which permission is not required) please go to the Copyright Clearance Center request page.

Read more about how to correctly acknowledge RSC content.

Social activity

Spotlight

Advertisements