A global model for long-range interaction `damping functions'

In recent years, `damping functions', which characterize the weakening of inverse-power-sum long-range interatomic interaction energies with increasing electron overlap, have become an increasing important component of models for diatomic molecule interaction potentials.\footnote{R.J.\ Le~Roy, C. C. Haugen, J. Tao and Hui Li, {\it Mol.\ Phys.}\ {\bf 109},435 (2011).} However, a key feature of models for damping functions, their portability, has received little scrutiny. The present work set out to examine all available {\it ab initio} induction and dispersion damping function data\footnote{P.J. Knowles and W.J. Meath,{\it J.\ Mol.\ Phys.}\ {\bf 60}, 1143 (1987)R.J. Wheatley and W.J. Meath,{\it J.\ Mol.\ Phys.}\ {\bf 80}, 25 (1993)R.J. Wheatley and W.J. Meath {\it J.\ Chem.\ Phys.}\ {\bf 179}, 341 (1994)R.J. Wheatley and W.J. Meath,{\it J.\ Chem.\ Phys.}\ {\bf 203}, 209 (1996).} and to attempt to devise a `global' scheme for diatomic molecule damping functions. It appears that while neutral (H, He, Li, and Ne, homonuclear and mixed) and anion (H$^-$ with H, He and Li) species obey (approximately) one common rule, proton plus neutral (H$^+$ with H, He and Li) and non-proton-cation plus neutral systems (He$^+$ and Li$^+$ with H, He and Li), must each be treated separately. However, for all three cases, a version of the Douketis-Scoles-Thakkar\footnote{C. Douketis,G. Scoles, S. Marchetti, M. Zen and A. J. Thakkar, {\it J.\ Chem.\ Phys.}\ {\bf 76}, 3057 (1982).} (ionization potential)$^{\rm power}$ factor is a key scaling parameter