Magic numbers for water-ammonia binary clusters: Enhanced stability of ion clathrate structures

The formation of water-ammonia binary clusters (H₂O)_n (NH₃)_m H⁺ (q≲40, q = n + m), have been investigated employing a neutral supersonic nozzle expansion of premixed water-ammonia gas with molecular-beam-mass spectrometry. The analysis of the mass spectra reveals that the number of water-rich clusters is greatly increased as the cluster size is increased. Mass spectroscopic evidence for the existence of enhanced structural stabilities ("magic numbers") has been found at the protonated clusters (H₂O)₂₀(NH₃) _m H⁺ (m = 1-6) and (H₂O)₂₇NH ₄⁺. Considerations for the magic number stabilities are presented within the framework of ion clathrate (ion-centered cage) structures. Monte Carlo simulations are also presented for ionized (protonated) clusters around n = 20 and n = 27 with m = 1. The clusters (H₂O) ₂₀NH₄⁺ and (H₂O)₂₇NH ₄⁺ have greater binding energies per molecule than their neighbors, in agreement with the mass spectroscopic observations. The calculated structure for (H₂O)₂₀NH₄⁺ also indicates the stability of pentagonal rings of water molecules and deformed dodecahedral structure with an NH₄⁺ ion trapped inside; the cluster is especially stable due not only to the strong Coulombic interaction (ionic hydrogen bonding) between the NH₄⁺ ion and the surrounding 20 water molecules but to hydrogen bonding networks forming the cage structure. The proposed ion-centered cage model can also explain satisfactorily the well-known stability of the water cluster of (H ₂O)₂₀H₃O⁺.