Effective ion-in-molecule potentials for non-penetrating rydberg states of polar molecules

Rydberg states of atoms or molecules for which the inner turning point of the Rydberg electron on the radial plus centrifugal potential lies outside the bulk of the ion core electron density are known as core-non-penetrating states. Interpretation of Rydberg spectroscopic data for polar molecules makes use of effective potentials that include ionic bonding and polarizability in order to represent electric properties of the ion core. We examine the accuracy and convergence properties of single-center polarization potentials and show that the center of charge representation, for which the core dipole moment is zero so that first-order l-mixing can be neglected, is excluded by the convergence sphere for use with l-states that can be treated by an expansion about the center or mass, the center of dipole or a newly-defined center of polarizability. The potential expansion converges only outside a sphere enclosing the charge distribution, and the sphere is much larger when the center of charge is used. For higher l-states of the rotating molecule (turning points defined in center of mass), the sphere required for convergence is much smaller for an origin within the charge distribution, so that lower l states are modeled correctly