  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 (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 (SC) 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.
