The structural stability and magnetic properties of the icosahedral Ni13, Ni13^＋1 and Ni13^-1 clusters have been obtained by utilizing all-electron density functional theory with the generalized gradient approximations for the exchange-correlation energy. The calculated results show that the ground states of neutral and charged clusters all favour a D3d structure, a distorted icosahedron, due to the Jahn-Teller effect. The radial distortions caused by doping one electron and by doping one hole are opposite to each other. Doping one electron will result in a 1/2 decrease and doping one hole will result in a 1/2 increase of the total spin. Both increasing interatomic spacing and decreasing coordination will lead to an enhancement of the spin magnetic moments for Nil3 clusters.
According to the one-dimensional tight-binding Su-Schrieffer-Heeger model, we have investigated the effects of charged polarons on the static polarizability, axx, and the second order hyperpolarizabilities, γxxxx, of conjugated polymers. Our results are consistent qualitatively with previous ab initio and semi-empirical calculations. The origin of the universal growth is discussed using a local-view formalism that is based on the local atomic charge derivatives. Furthermore, combining the Su Schrieffer-Heeger model and the extended Hubbard model, we have investigated systematically the effects of electron-electron interactions on αxx and γxxxx of charged polymer chains. For a fixed value of the nearest-neighbour interaction V, the values of αxx and γxxxx increase as the on-site Coulomb interaction U increases for U 〈 Uc and decrease with U for U 〉 Uc, where Uc is a critical value of U at which the static polarizability or the second order hypcrpolarizability reaches a maximal value of αxx or γxxxx. It is found that the effect of the e-e interaction on the value of αxx is dependent on the ratio between U and V for either a short or a long charged polymer. Whereas, that effect on the value of γxxxx is sensitive both to the ratio of U to V and to the size of the molecule.
