Discussion and Comparison of Particular Cases

Having described the variety of ways in which the core-valence interaction may be parameterized it is clear that we should examine how they perform in actual calculations. Generally the advances in the complexity of the parameterization have produced commensurate improvements in the accuracy of the results. However, by introducing a large number of parameters the simplicity of the core-valence concept is lost and, in practice, the fitting of the parameters themselves can be expensive in terms of computer time, although they only need to be obtained once for each atom. 

From the tables of results which follow, two sorts of comparison can be drawn firstly the pseudopotential calculation involving the valence electrons (VE) can be compared with the all-electron (AE) calculation in the same basis set, and secondly both the AE and the VE calculations can be compared either with experimental quantities or, what is possibly better here, with an AE calculation in a very large ( Hartree-Fock limit ) basis so that the eigenvalues may be compared. The former comparison reveals how well the pseudopotential allows the VE calculation to reproduce the AE one, given that they both have essentially the same flexibility in the valence space, and the latter shows how the small basis set calculations may differ 

The calculations described below have been selected from the extensive recent literature on pseudopotential calculations as examples which allow these comparisons. 

The method of Kahn, Goddard, et al is probably the most exact representation of the local class of pseudopotentials, and it is thus interesting to compare their results with those calculated using the Reporters own non-local representation, which is one of the more exact of this type. Values of the ionization energies and eigenvalues of the iron atom and its positive ions are presented in Table 3 and for (FeH)+ in Table 4. 81 Attempts were made to make the calculations as comparable 

The semi-local pseudopotential24 used for the calculations of Table 3 was based on a parameterization for the neutral atom. Melius, Olafson, and Goddard also included in their paper some calculations based on the single valence electron ion Fe7+. As expected, this parameterization leads to far worse results, which differ on average from the all-electron results by 0.05 a.u., thus emphasizing the importance of the contribution of valence-valence interaction to the effective potential [equation (51)]. 

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