Applications of computational geometry to the molecular simulation of interfaces

TL;DR

This paper introduces a novel computational geometry approach using alpha-shapes to identify interfacial molecules in fluid-fluid simulations, providing a new perspective on a longstanding problem.

Contribution

It applies alpha-shape concepts to molecular simulation, offering a new method for defining interfacial molecules based on geometric shape analysis.

Findings

The alpha-shape method effectively identifies interfacial molecules.

Results are consistent with previous methods, validating the approach.

The method offers a flexible parameter for shape definition.

Abstract

The identification of the interfacial molecules in fluid-fluid equilibrium is a long-standing problem in the area of simulation. We here propose a new point of view, making use of concepts taken from the field of computational geometry, where the definition of the "shape" of a set of point is a well-known problem. In particular, we employ the $\alpha$-shape construction which, applied to the positions of the molecules, selects a shape and identifies its boundary points, which we will take to define our interfacial molecules. A single parameter needs to be fixed (the "$\alpha$" of the $\alpha$-shape), and several proposals are examined, all leading to very similar choices. Results of this methodology are evaluated against previous proposals, and seen to be reasonable.