Optimized Monotonic Convex Pair Potentials Stabilize Low-Coordinated Crystals

2010/10/29 by Étienne Marcotte, Marcotte, Etienne, Frank H. Stillinger +3 · 1 citation
Chemistry · Materials Science · #Block Copolymer Self-Assembly #Electrostatics and Colloid Interactions #FOS: Physical sciences #Material Dynamics and Properties #Soft Condensed Matter (cond-mat.soft) #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1010.6293

openalex publication_date 2010/10/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We have previously used inverse statistical-mechanical methods to optimize isotropic pair interactions with multiple extrema to yield low-coordinated crystal classical ground states (e.g., honeycomb and diamond structures) in d-dimensional Euclidean space R^d. Here we demonstrate the counterintuitive result that no extrema are required to produce such low-coordinated classical ground states. Specifically, we show that monotonic convex pair potentials can be optimized to yield classical ground states that are the square and honeycomb crystals in R² over a non-zero number density range. Such interactions may be feasible to achieve experimentally using colloids and polymers.

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