Electronic structure of calcium clusters

Abstract

The electronic structure of calcium clusters containing up to 13 atoms is studied within the general gradient approximation (GGA) of the density-functional formalism. For the calcium dimer it is observed that the exchange functional in GGA overestimates the binding energy, while a hybrid approach including Hartree-Fock exchange gives a better agreement with the experimental results. Binding energies, optimized geometries, vibrational frequencies, and thermodynamic properties have been calculated for several isomers at each cluster size. Various structures corresponding to saddle points of the energy curve are reported, along with the isomerization reaction path for ${\mathrm{Ca}}_{5},$ ${\mathrm{Ca}}_{6},$ and ${\mathrm{Ca}}_{7}.$ It was found that ${\mathrm{Ca}}_{12}$ undergoes a structural transition as a function of temperature, changing structure at T=317 K. A comparison of the minimum energy isomer geometry and binding energy obtained for each cluster size with those obtained from the Murrell-Mottram empirical potential shows that this potential overestimates the binding energies and does not adequately predict the optimized structures for several cluster sizes.