Quantum-based models of charge-dependent potential energy surfaces: Three-state models

Quantum-based models of how potential energies depend on charge are developed from a three-state model, at the level of neglecting state-to-state overlap. The energy as a function of charge is defined as proposed previously (Valone and Atlas, J Chem Phys 2004, 120, 7262). With this definition, addition of a third state smooths the derivatives of the energy model with respect to charge at integer values of charge that are in the interior of the allowed charge range. These derivatives are related to the chemical potential. At the dissociation limit, this model converges to established limits. Another dependence is proposed that uses two different charges simultaneously. The concepts are illustrated, with calculations on an OH molecule.