Stable geometries and electronic structures of ammonia cluster ions NH4/+(NH3)(n-1) (n = 1-17) are investigated by the ab initio theory in order to clarify the origin of the observed magic number. Since the ammonium ion NH4/+ brings about a large attraction to ammonia monomers, the stable geometries of NH4/+(NH3)(n-1) (n = 1-17) have shell structures around the ion. The calculated binding energy, which well reproduces the experimental ones, decreases monotonically as the cluster size increases. Gibbs free energies are also estimated with the use of the calculated electronic and vibrational energies. The Gibbs free energy curve with respect to the cluster size gives a minimum at n = 5 in comparatively wide temperature and pressure region, which corresponds to the experimental magic number. The minimum is found to be due to two competitive factors; that is, the nonlinear aspect of the binding energy and the linear instability of the translational entropy as the cluster size increases. (C) 2000 Elsevier Science B.V.
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