The Parameterization of Pseudopotentials

Having reviewed the theoretical background to the core-valence separation, we now turn to the practical implementation of the theory. Starting from equations (31)— (34) we note that the valence pseudo-orbitals are eigenfunctions of an equation which can be written as 

Some of the more common parameterizations are illustrated by the following examples. Heilman6 assumed 

Similar to the Heilman approach are the potentials listed below  

In the last three cases above the authors have made the radial form of the potential dependent on the angular part of the wavefunction on which it operates, recognizing that the potential experienced by an electron in, for example, the 3p orbital of chlorine is different from that in the 3s. Such potentials are termed semi-local. This dependence is particularly important when there are valence orbitals in an atom which have angular momenta which are not present in the core, e.g. the 3d orbital of the first row of transition metals. 

The complexity of the functional form for Cc0Te increases from equation (67) to equation (71). To remove the necessity of accepting any particular predetermined functional form Kahn and Goddard29 evaluated a semi-local potential by making use of 

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