Mikael C. Rechtsman,¹ Frank H. Stillinger,² and Salvatore Torquato^2,3,4,5

¹ Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
² Department of Chemistry, Princeton University, Princeton, New Jersey 08544, USA
³ Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544, USA
⁴ Princeton Institute for the Science and Technology Materials, Princeton University, Princeton, New Jersey 08544, USA
⁵ Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544, USA

(Received 7 May 2006; published 7 August 2006)

Phys. Rev. E 74, 021404 (2006)

Abstract

Conventional wisdom presumes that low-coordinated crystal ground states require directional interactions. Using our recently introduced optimization procedure to achieve self-assembly of targeted structures [M. C. Rechtsman et al., Phys. Rev. Lett. 95, 228301 (2005); Phys. Rev. E 73, 011406 (2006)], we present an isotropic pair potential V(r) for a three-dimensional many-particle system whose classical ground state is the low-coordinated simple cubic lattice. This result is part of an ongoing pursuit by the authors to develop analytical and computational tools to solve statistical-mechanical inverse problems for the purpose of achieving targeted self-assembly. The purpose of these methods is to design interparticle interactions that cause self-assembly of technologically important target structures for applications in photonics, catalysis, separation, sensors, and electronics. We also show that standard approximate integral-equation theories of the liquid state that utilize pair correlation function information cannot be used in the reverse mode to predict the correct simple cubic potential. We report in passing optimized isotropic potentials that yield the body-centered-cubic and simple hexagonal lattices, which provide other examples of non-close-packed structures that can be assembled using isotropic pair interactions.