  Using inverse statistical-mechanical optimization techniques, we have
discovered isotropic pair interaction potentials with strongly repulsive cores
that cause the tetrahedrally coordinated diamond and wurtzite lattices to
stabilize, as evidenced by lattice sums, phonon spectra, positive-energy
defects, and self-assembly in classical molecular dynamics simulations. These
results challenge conventional thinking that such open lattices can only be
created via directional covalent interactions observed in nature. Thus, our
discovery adds to fundamental understanding of the nature of the solid state by
showing that isotropic interactions enable the self-assembly of open crystal
structures with a broader range of coordination number than previously thought.
Our work is important technologically because of its direct relevance generally
to the science of self-assembly and specifically to photonic crystal
fabrication.
