An improved Hellmann-type pseudopotential for atoms and molecules

The concept of pseudopotentials offers much attractiveness for the quantum mechanical evaluation of the physical properties of atoms and molecules. The ideas of Hellmann, in which the repulsive and fermion character of inner electrons can be mimicked by an experimentally fitted, exponentially damped potential term, are especially attractive. Unfortunately, it is found that such a simple expression can only be used in a very limited number of cases, such as for the alkali metals, and even then fails for the simple case of lithium. The present study shows that the Hellmann idea can readily be extended by including a second “shielded potential” term evaluated from tabulated previous Hartree-Fock calculations. The new expression for the model pseudopotential is both simple and effective. With it, the inner potential of any of the alkali metal atoms, including lithium, can be represented so that calculation of the molecular properties of the metal dimers can be accomplished. Calculations for Li₂, Na₂, and K₂ show the binding energies and equilibrium interatomic distances to be quite well given, in agreement with both chemical experience and spectroscopic evidence.