A Computational Study of 3‐D Helium Clusters

Physical and thermodynamic properties have been calculated and analyzed for the best and optimized geometries of the 3‐D clusters with N = 3 to N = 10 atoms and unit cells of three types of crystalline systems using ab initio RHF/6–31G^** method. Dependence of the lattice binding energy on the cluster parameter, R, has been studied. Similar behavior observed for the binding energies for all clusters shows that probabilities of their existence in the condensed phase are more or less the same. In the next step, thermodynamic properties have been calculated and analyzed for He₂₇ 3‐D helium clusters with simple cubic, body centered cubic (bcc), trigonal and hexagonal (hcp) configurations. The results show that the hexagonal cluster is more favored over other clusters. It is found that these clusters are electronically stable over a limited range of the values for the lattice parameter. Δ_fH is constant in this stability region and thus the Δ_fG exactly follows the variations of TΔ_fS. Surface effects have been investigated by comparing the square and hexagonal He₉ 2‐D lattices with the cubic and hexagonal He₂₇ 3‐D lattices, respectively. The lattice parameters, densities and molar volumes calculated for the clusters with hcp and bcc configurations have satisfactory agreement with the available experimental values. Properties of the He₁₃, He₃₄ and He₁₀₄ hcp clusters have also been calculated and analyzed.