Examining the cubic, fused cubic, and cage structures of (H₂O)_n for n = 8, 9, 12, 16, 20, and 21: Do fused cubic structures form?

The structures and stabilization energies (SE) of water clusters, (H₂O)_n, with n = 8, 9, 12, 16, 20, and 21, were calculated by applying the intermediate neglect of differential overlap self-consistent field restricted Hartree-Fock method (INDO SCF RHF) after proper parametrization. These cluster structures include the neutral cubic forms for 8 and 9 mers, fused cubic 12, 16, 20, and 21 mers and cage structures for 16, 20, and 21 mers. In addition, the structure and SE values of the protonated fused cubic 20 and 21 mer clusters were calculated and compared with those of the cage structures. A closer examination of the fused cubic and the cage structures combined with the experimental evidence suggests that the fused structures are not likely to form. The present study also explains the observed magic numbers in experiments.