A new topological descriptor for water network structure.

Bulk water molecular dynamics simulations based on a series of atomistic water potentials (TIP3P, TIP4P/Ew, SPC/E and OPC) are compared using new techniques from the field of topological data analysis. The topological invariants (the different degrees of homology) derived from each simulation frame are used to create a series of persistence diagrams from the atomic positions. These are averaged over the simulation time using the persistence image formalism, before being normalised by their total magnitude (the L1 norm) to ensure a size independent descriptor (L1NPI). We demonstrate that the L1NPI formalism is suitable for the analysis of systems where the number of molecules varies by at least a factor of 10. Using standard machine learning techniques, a basic linear SVM, it is shown that differences in water models are able to be isolated to different degrees of homology. In particular, whereas first degree homology is able to distinguish between all atomistic potentials studied, OPC is the only potential that differs in its second degree homology. The L1 normalised persistence images are then used in the comparison of a series of Stillinger-Weber potential simulations to the atomistic potentials and the effects of changing the strength of three-body interactions on the structures is easily evident in L1NPI space, with a reduction in variance of structures as interaction strength increases being the most obvious result. Furthermore, there is a clear tracking in L1NPI space of the λ parameter. The L1NPI formalism presents a useful new technique for the analysis of water and other materials. It is approximately size-independent, and has been shown to contain information as to real structures in the system. We finally present a perspective on the use of L1NPIs and other persistent homology techniques as a descriptor for water solubility.