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Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics

Author(s): Zhang, Ge; Stillinger, Frank H.; Torquato, Salvatore

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Abstract: Inverse statistical-mechanical methods have recently been employed to design optimized short-range radial (isotropic) pair potentials that robustly produce novel targeted classical ground-state many-particle configurations. The target structures considered in those studies were low-coordinated crystals with a high degree of symmetry. In this paper, we further test the fundamental limitations of radial pair potentials by targeting crystal structures with appreciably less symmetry, including those in which the particles have different local structural environments. These challenging target configurations demanded that we modify previous inverse optimization techniques. In particular, we first find local minima of a candidate enthalpy surface and determine the enthalpy difference ΔH between such inherent structures and the target structure. Then we determine the lowest positive eigenvalue λ0 of the Hessian matrix of the enthalpy surface at the target configuration. Finally, we maximize λ0ΔH so that the target structure is both locally stable and globally stable with respect to the inherent structures. Using this modified optimization technique, we have designed short-range radial pair potentials that stabilize the two-dimensional kagome crystal, the rectangular kagome crystal, and rectangular lattices, as well as the three-dimensional structure of the CaF2 crystal inhabited by a single-particle species. We verify our results by cooling liquid configurations to absolute zero temperature via simulated annealing and ensuring that such states have stable phonon spectra. Except for the rectangular kagome structure, all of the target structures can be stabilized with monotonic repulsive potentials. Our work demonstrates that single-component systems with short-range radial pair potentials can counterintuitively self-assemble into crystal ground states with low symmetry and different local structural environments. Finally, we present general principles that offer guidance in determining whether certain target structures can be achieved as ground states by radial pair potentials. © 2013 American Physical Society.
Publication Date: Oct-2013
Electronic Publication Date: 23-Oct-2013
Citation: Zhang, G, Stillinger, FH, Torquato, S. (2013). Probing the limitations of isotropic pair potentials to produce ground-state structural extremes via inverse statistical mechanics. Physical Review E, 88 (4), 10.1103/PhysRevE.88.042309
DOI: doi:10.1103/PhysRevE.88.042309
ISSN: 1539-3755
EISSN: 1550-2376
Pages: 88, 042309-1 - 042309-15
Type of Material: Journal Article
Journal/Proceeding Title: Physical Review E
Version: Final published version. Article is made available in OAR by the publisher's permission or policy.
Notes: Volume 88, Issue 4, 23 October 2013, Article number 042309

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