Arkus, NatalieManoharan, VinothanBrenner, Michael2009-12-102009Arkus, Natalie, Vinothan N. Manoharan, Michael P. Brenner. 2009. Minimal energy clusters of hard spheres with short range attractions. Physical Review Letters 103(11): 118303.0031-9007http://nrs.harvard.edu/urn-3:HUL.InstRepos:3443104We calculate the ground states of hard-sphere clusters, in which n identical hard spherical particles bind by isotropic short-ranged attraction. Combining graph theoretic enumeration with basic geometry, we analytically solve for clusters of n<or=10 particles satisfying minimal rigidity constraints. For n<or=9 the ground state degeneracy increases exponentially with n, but for n>9 the degeneracy decreases due to the formation of structures with >3n-6 contacts. Interestingly, for n=10 and possibly at n=11 and n=12, the ground states of this system are subsets of hexagonal close-packed crystals. The ground states are not icosahedra at n=12 and n=13. We relate our results to the structure and thermodynamics of suspensions of colloidal particles with short-ranged attractions.en-USJournal Article2009-12-1010.1103/PhysRevLett.103.118303