Unusual ground states via monotonic convex pair potentials

É Marcotte, F. H. Stillinger, S. Torquato

Research output: Contribution to journalArticlepeer-review

35 Scopus citations


We have previously shown that inverse statistical-mechanical techniques allow the determination of optimized isotropic pair interactions that self-assemble into low-coordinated crystal configurations in the d-dimensional Euclidean space Rd. In some of these studies, pair interactions with multiple extrema were optimized. In the present work, we attempt to find pair potentials that might be easier to realize experimentally by requiring them to be monotonic and convex. Encoding information in monotonic convex potentials to yield low-coordinated ground-state configurations in Euclidean spaces is highly nontrivial. We adapt a linear programming method and apply it to optimize two repulsive monotonic convex pair potentials, whose classical ground states are counterintuitively the square and honeycomb crystals in R2. We demonstrate that our optimized pair potentials belong to two wide classes of monotonic convex potentials whose ground states are also the square and honeycomb crystal. We show that these unexpected ground states are stable over a nonzero number density range by checking their (i) phonon spectra, (ii) defect energies and (iii) self assembly by numerically annealing liquid-state configurations to their zero-temperature ground states.

Original languageEnglish (US)
Article number164105
JournalJournal of Chemical Physics
Issue number16
StatePublished - Apr 28 2011

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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