Long-range damping functions improve the short-range behaviour of ‘MLR’ potential energy functions

Abstract

The recently introduced [Mol. Phys. 105, 663 (2007)] ‘Morse/long-range’ (or MLR) potential energy function is a very flexible form which explicitly incorporates the theoretically predicted inverse-power-sum long-range tail, is smooth and differentiable everywhere, and includes the well depth , equilibrium distance r _e, and long-range interaction coefficients C_m as explicit parameters. This form is being used increasingly commonly in direct-potential-fit analyses of experimental data. The present work shows that the MLR form can readily accommodate the inclusion of ‘damping functions’ in the description of the long-range potential tail, and that inclusion of such terms leads to much more realistic short-range extrapolation behaviour. Illustrative applications to the ground electronic states of MgH, Li₂ and ArXe are presented.

Keywords:

• potential energy function
• damping functions
• MgH
• Li₂(X)
• ArXe

Acknowledgements

We are pleased to acknowledge helpful discussions with Professors F.R.W. McCourt and M. Nooijen. This research was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC).

Notes

Notes

1. The one exception is the treatment of the state of Li₂ in 26, for which is determined by diagonalizing a matrix of simple inverse-power terms associated with two coupled states.

2. The terminology ‘expanded’ versus ‘non-expanded’ reflects the fact that the derivation of Equation (7) is based on the assumption that the Coulomb interaction between the electrons of one atom and the electrons and nucleus of the other could be expanded in terms of inverse powers of the internuclear separation.

3. On the scale of Figure 2, most of the curves corresponding to modified Tang–Toennies damping functions for s = 2 are indistinguishable from the curves for the three sets of modified Douketis-type functions. However, the modified Tang–Toennies functions for s = 3 give a distinctly worse fit for which .

4. The parameter values shown here differ slightly from those reported in 45 because it was later found that additional terms should have been included in the expression describing the centrifugal Born–Oppenheimer breakdown radial strength function, and that extended model is used here.

5. It is necessary to use different basis sets for the two atoms in order to avoid linear correlation of the basis sets at very short range.