Parameter-free coordination numbers for solutions and interfaces

Coordination numbers are among the central quantities to describe the local environment of atoms and are thus used in various applications such as structure analysis, fingerprints, and parameters. Yet, there is no consensus regarding a practical algorithm, and many proposed methods are designed for specific systems. In this work, we propose a scale-free and parameter-free algorithm for nearest neighbor identification. This algorithm extends the powerful Solid-Angle based Nearest-Neighbor (SANN) framework to explicitly include local anisotropy. As such, our Anisotropically corrected SANN (ASANN) algorithm provides with a fast, robust, and adaptive method for computing coordination numbers. The ASANN algorithm is applied to flat and corrugated metallic surfaces to demonstrate that the expected coordination numbers are retrieved without the need for any system-specific adjustments. The same applies to the description of the coordination numbers of metal atoms in AuCu nanoparticles, and we show that ASANN based coordination numbers are well adapted for automatically counting neighbors and the establishment of cluster expansions. Analysis of classical molecular dynamics simulations of an electrified graphite electrode reveals a strong link between the coordination number of Cs⁺ ions and their position within the double layer, a relation that is absent for Na⁺, which keeps its first solvation shell even close to the electrode.