Structure and stability of sodium-doped helium snowballs through DFT calculations

The lowest energy structures and relative stabilities of pure and sodium-doped helium clusters Na+Hen have been determined using DFT calculations. Firstly, a series of DFT functionals have been tested by the calculation of the potential energy curve of the Na+-He system in order to find the most suitable and reliable method for studying the Na+Hen clusters. The calculations showed that the M05-2X functional combined with the extended polarized and diffused Pople basis set 6-311++G(d,p) reproduce correctly the experimental Na+-He potential energy curve. Hence, the most stable geometries of Na+Hen clusters up to n = 20 have been optimized at M05-2X/6-311++G(d,p) level. An icosahedral geometry is obtained for the Na+He12 ensuring the closure of the first solvation shell and forming the so-called 'Snowballs' feature. The relative stabilities of the Na+Hen clusters are discussed on the basis of the dependence of the binding energy, fragmentation energy and second-order difference of energy as well as the HOMO-LUMO energy gap with the size of the clusters. The clusters Na+He8, Na+He9 and Na+He12 are found to be relatively more stable than their neighbors. The snowball formation was explained through natural population analysis. The non-covalent interaction NCI analysis was performed on the basis of the reduced density gradient RDG. Finally, binding enthalpy, entropy and Gibbs free energy are calculated and showed that the formation process of Na+Hen clusters is endothermic.