The Full-size image (<1 K) clusters have been studied using ab initio calculations. For n=0 and 1, the geometry of clusters are optimized at B3LYP, MP2, CCD and QCISD levels with several basis sets, and the binding energies are compared to experimental results to find the reliable and less computationally demanding methods for the calculations of larger clusters. For n=2–6, the geometry optimizations and NH stretching vibrational spectra are performed at B3LYP and MP2 levels with 6-31+G* basis set. The binding energies are corrected by basis set superposition errors (BSSE) and zero-point vibrational energies (ZPVE). These two approaches that correspondingly predict the filled first solvation shell are the lowest in energies at n=1–4. The vibrational frequency shift of ammonium molecules have been investigated along with the frequency characteristics depending on the presence/absence of outer-shell ammonia molecules. In this study, the calculated binding energies and the characteristic NH stretching vibrational frequency shift are in good agreement with experimental data. In addition, the barriers of proton transfer between two heavy atoms and the internal rotation of ammonia molecular along the NH axis in NH4+(NH3)n are estimated with several levels.
