In this research project, supported by a Career Advancement Award for Women Scientists, high-level, ab initio, molecular electronic structure calculations will be carried out for clusters consisting of one or more metal atoms, particularly Hafnium, inside or outside a cage of 28 carbon atoms. The calculations will be carried out with relativistic core potentials, spin-orbit operators, large orbital basis sets, and a configuration interaction wavefunction. The COLUMBUS code will be used taking maximum advantage of the high point group symmetry of the molecular system. The results will be analyzed to predict trends in ionization potentials, electron affinity, and electronic spectra, and to study the factors that affect chemical bonding in these fullerene-like cluster compounds. The recent discovery of Buckminsterfullerene, a remarkably stable molecule consisting of 60 carbon atoms forming a symmetric cage resembling a soccer ball, has motivated experiments to find other molecules with similar chemical bonding. One of the smallest such carbon cluster molecules, observed in plasmas, consists of 28 carbon atoms bonded together, as in Buckminsterfullerene, in fused rings of five and six atoms around a heavy metal atom. A few of these 28 carbon atom complexes are selected for theoretical study using highly accurate quantum mechanical theory to predict physical properties which will aid the interpretation of experiments and provide a deeper understanding of the chemical principles which govern the stabilities of such complexes