A method for modeling a material at least partially-defined by atomic information includes, for each of a plurality of configurations of the material, determining energy moments for a density of states of the respective configuration of the material, and generating a tight binding Hamiltonian matrix for the respective configuration of the material. The method further includes, for each of the plurality of configurations of the material, forming a tight binding model of the configuration of the material by resolving a linking of (i) the energy moments for the density of states of the material to (ii) the tight binding Hamiltonian matrix for the material. Still further the method includes, based on the tight binding models for each of the configurations of the material, forming an environmentally-adapted tight binding model.