A symmetric structure of the gas-phase H3+(H2)9 cluster

Structures of the gas-phase clusters, H3+(H2)n (n=0–10) and binding energies of H3+(H2)n and D3+(D2)n (n=1–9) were calculated with a modified G2 theory, called G2* here. Theoretical binding energies and their isotope effects are in good agreement with experimental data. Shell structures were examined carefully. The n=7 cluster is the second half-shell where one H2 molecule above the H3+(H2)3 first solvation shell and three below the shell. The H3+(H2)9 cluster is the complete second shell. The C3-symmetry condition is required to form shells. Therefore, the `magic numberʹ n=6 is not effective in the H3+(H2)n cluster.