Localized states of an excess electron in ionic clusters
  A theory for an electron affinity of ionic clusters is proposed both in a quasiclassical approach and with quantization of a polarization electric field in a nanoparticle. An interaction of an electron with longitudinal optical phonons in an ionic cluster is described. A critical size of the cluster regarding in formation of an electron's autolocalized state, dependencies of an energy and a radius of a polaron on a cluster's size are obtained by a variational method. It has been found that a binding energy of the electron in a cluster depends on a cluster's radius but the radius of electron's autolocalization does not depend on cluster's radius and equals to the polaron radius in a corresponding infinity crystal, moreover the bound state of the electron in a cluster is possible if the cluster's radius is more then the polaron radius. A perturbation method for finding of the critical parameters is proposed, where an dependence of the critical size on a momentum of an electron in a conduction band is observed. 
K.V. Grigorishin, B.I. Lev
cond-mat.mes-hall