Structure and properties of theNi@Si12cluster from all-electronab initiocalculations

Abstract

The structural, electronic, and vibrational properties of the $\mathrm{Ni}@{\mathrm{Si}}_{12}$ cluster have been studied using all-electron ab initio calculations in the framework of the density functional theory (DFT) with the hybrid nonlocal exchange and correlation functional of Becke-Lee-Yang-Parr (B3LYP). Perturbation theory was also used for the lowest energy competing structures in order to unambiguously identify the ground state in view of marginal total energy differences at the DFT/B3LYP level of theory. To facilitate possible future experimental identification and to check the stability of the structures, we have performed vibrational analyses that include Raman and infrared spectra for the stable structures. Through the vibrational analysis, we have found that the ${C}_{5v}$ symmetric Frank-Kasper structure, based on an icosahedral structural motif, which for some time was believed as the ground state, is unstable. Our calculations reveal a ground state of ``cubic'' ${D}_{2d}$ symmetry, which at the fourth order of perturbation theory is about $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ lower than the alternative suggested ground state, based on a hexagonal structural motif. This distorted hexagonal structure of ${C}_{\mathrm{S}}$ symmetry at the DFT/B3LYP level of theory is practically isoenergetic to our cubic ${D}_{2d}$ structure, with a marginal energy difference of about $0.04\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. In addition to IR and Raman spectra, we have examined in detail electronic (bonding and binding), structural, and chemical characteristics that could be important for possible future applications of these or derived from these materials. Such characteristics include total and partial density of states, crystal orbital overlap populations, binding energies, ionization potentials, electron affinities, ``chemical hardness,'' and embedding energies.