Maximum probability domains for the analysis of the microscopic structure of liquids

TL;DR

This paper introduces maximum probability domains (MPDs) as a novel method to analyze the microscopic spatial structure of liquids, providing insights into local arrangements and solvation shells.

Contribution

The paper develops the concept of MPDs for liquids and implements a level set method to identify regions with maximum particle probability, applying it to water and sodium solvation.

Findings

MPDs reveal detailed local structures of water at different pressures.

MPDs provide new insights into solvation shells of sodium in water.

The method effectively characterizes microscopic arrangements in liquids.

Abstract

We introduce the concept of maximum probability domains (MPDs), developed in the context of the analysis of electronic densities, in the study of the microscopic spatial structures of liquids. The idea of locating a particle in a three dimensional region, by determining the domain where the probability of finding that, and only that, particle is maximum, gives an interesting characterization of the local structure of the liquid. The optimization procedure, required for the search of the domain of maximum probability, is carried out by the implementation of the level set method. Results for a couple of case studies are presented, to illustrate the structure of liquid water at ambient conditions and upon increasing pressure from the point of view of MPDs and to compare the information encoded in the solvation shells of sodium in water with, once again, that extracted from the MPDs.