Ab initio and Monte Carlo study of the structure and stability of H₃⁺(H₂)_n (n = 3-16)

The molecular geometries of hydrogen cluster ions, H₃⁺(H₂)_n (n = 3-16), were investigated by using the classical Monte Carlo and annealing method. The two-body potential functions were obtained by fitting the results of ab initio MP4(SDTQ) calculations. Molecular structure and stability are mainly determined by an ionic interaction between H₃⁺ and H₂. The H₂-H₂ interaction forces H₂ molecules to stay away from each other but seems to have little effect upon the structure and stability of clusters in the vicinity of the equilibrium structure. The n dependency of the binding energy (-ΔE_n-1,n) is in good agreement with the experimental trend in -ΔH_n-1,n known for n ≤ 9. Magic numbers in the stabilization energy have been found at n = 3, 6, 9, 12, and 15, where optimized molecular structures are closed shells with 3-fold symmetry and have one to five layers of (H₂)₃ solvation shells over the H₃⁺ core.