Structure, stability, and infrared spectroscopy of $(H2O)nNH4+$ clusters: A theoretical study at zero and finite temperature

The combined effects of size and temperature on the stable structures of water clusters doped with one ammonium molecule have been investigated theoretically using an empirical potential and density-functional theory (DFT) calculations. Global optimization with Monte Carlo methods has been performed using an explicit intermolecular potential based on the Kozack–Jordan polarizable model. Putative lowest-energy structures based on this empirical potential are reported. Our results indicate a high propensity for the $NH4+$ impurity to be fully solvated by water molecules. Clathratelike patterns are formed for clusters containing more than 11 molecules. Local reoptimizations of candidate structures carried out at the DFT level with the B3LYP hybrid functional and the $6-311++G(d,p)$ basis set confirm the general trends obtained with the intermolecular potential. However, some reorderings between isomers often due to zero-point energy corrections are found in small clusters, leading to stable geometries in agreement with other first-principles studies. Temperature effects have been assessed using a simple harmonic superposition approximation for selected cluster sizes and using dedicated Monte Carlo simulations for $(H2O)20NH4+$⁠. The clusters are found to melt near 200 K, and possibly isomerize already below 50 K. The free energy barrier for core/surface isomerization of the impurity in the 21-molecule cluster is estimated to be only a few kcal/mol at 150 K. The vibrational spectroscopic signatures of the clusters obtained from the electronic structure calculations show the usual four O–H stretching bands. As the cluster size increases, the double acceptor-single donor band near $3700cm−1$ increasingly dominates over the three other bands. While we do not find conclusive evidence for a O–H stretching spectroscopic signature of the ammonium impurity to be in the core or at the surface in the 20-molecule cluster, a possible signature via the N–H stretching bands is suggested near $2800–2900cm−1$⁠. In the larger $(H2O)49NH4+$ cluster, the impurity is slightly more stable at the surface.