LAUSR

The lowest energy structures and relative stabilities of pure and sodium-doped helium clusters Na + He n 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 + He n 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 + He n 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 + He 12 ensuring the closure of the first solvation shell and forming the so-called ‘Snowballs’ feature. The relative stabilities of the Na + He n 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 + He 8 , Na + He 9 and Na + He 12 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 + He n clusters is endothermic.