Morphing Lennard-Jones clusters to TIP4P water clusters: Why do water clusters look like they do?

Cluster structures with globally minimal energy have been determined for a potential that was varied smoothly between an isotropic Lennard-Jones pair potential and the full TIP4P water potential, for cluster sizes between 4 and 22 molecules. Intermediate rhombohedral structures have been discovered that directly link the close-packed Lennard-Jones structures with the typical water cluster building blocks, explaining the occurence of the latter. Among these rhombohedral intermediates are the highly symmetric rhombic dodecahedron, which seeds the typical water-centered cage structures, and a 6-ring nanotube around a water dimer, which is directly related to the Lennard-Jones double icosahedron. The known qualitative defect of the TIP4P potential (preference of empty prismatic structures over molecule-centered cages at larger cluster sizes) would almost disappear at a 30% damping of the Coulomb term, without deterioration of the results at other cluster sizes.