Quantum Mechanical Origins of the Iczkowski-Margrave Model of Chemical Potential

Charge flow in materials at the atomistic level is controlled through chemical potential equalization among its constituents. Consequently employing this concept in a simulation requires some model of chemical potential. Current atomistic models of chemical potential, such as the Iczkowski-Margrave (IM) model, are built largely on heuristic arguments and depend linearly on the net charge of each constituent. To gain new insight into the IM model, a many-electron model Hamiltonian is constructed at the atomistic level that is commensurate with the IM model, as opposed to one designed at the one-electron level. For a three-state, two-fragment system, the essential electronegativity and the chemical hardness energies are recovered. However, the model Hamiltonian imparts new charge dependencies not found in the IM model. Decidedly nonlinear, transitional or hopping contributions in those new dependencies are shown to be critical to regulating charge flow. Other modifications to the IM model are illustrated with simple two- and three-fragment systems, involving as many as five states, that act as paradigms for general materials models. Including more than three states in the three-fragment example introduces local bonding refinements to the Mulliken electronegativity and chemical hardness.