Nuclear fuels and materials present special problems to atomistic-scale modeling. At a metal-metal-oxide interface, the metal centers are charged on the oxide side, but neutral on the metallic side. The intimate contact necessitates that atomistic models for these materials be both compatible and consistent with one another at some level. A new "fragment’’ Hamiltonian (FH) model, at the atomistic level, is presented that reduces qualitatively to existing, successful models for metals, such as the embedded atom method, and ceramics, such as the charge equilibration models. Moreover, the FH model possesses both electron hopping and fundamental gaps that appear as separate terms in a generalized embedding function. The electron hopping contributions come from both one-electron and two-electron sources. These contributions appear as a result of the FH point of view, rather than being postulated. The model obeys certain wellknown theoretical limits that come from the nonlinearity of electron hopping processes as the volume of a crystal is changed. The generalized notion of embedding entails two variables instead of one. The ability to account for multiple charge states in the cations leads to the capability within the model to distinguish the qualitative differences among metallic, ionic, and covalent bonding environments. The details of all of these energies, among with fragmentfragment interactions, combine to determine the state of the atom in the material.