Generalized Phillips-Kleinman Pseudopotential

Using the so-called generalized Phillips-Kleinman pseudopotential [3]... 

The generalization of the pseudopotential method to molecules was done by Boni-facic and Huzinaga[3] and by Goddard, Melius and Kahn[4] some ten years after Phillips and Kleinman s original proposal. In the molecular pseudopotential or Effective Core Potential (ECP) method all core-valence interactions are approximated with l dependent projection operators, and a totally symmetric screening type potential. The new operators, which are parametrized such that the ECP operator should reproduce atomic all electron results, are added to the Hamiltonian and the one electron ECP equations axe obtained variationally in the same way as the usual Hartree Fock equations. Since the total energy is calculated with respect to this approximative Hamiltonian the separability problem becomes obsolete. 

Note that this is just the same condition under which the generalized pseudopotential of Weeks, Hazi, and Rice13 reduced to the Phillips-Kleinman form.7)... 

Early work based on a statistical treatment of the core electrons was published by Hellmaim (1935) and Gombas (1935) for molecular and solid-state physics, respectively. Quantum-mechanical justifications in the framework of the Hartree and Hartree-Fock theories were given by Fenyes (1943) and Szepfalusy (1955, 1956), respectively. The first derivation of the pseudopotential approach within the Hartree-Fock formalism which came to general attention is due to Phillips and Kleinman (1959) and was later generalized by Hazi and Rice (1968). The accuracy and limitations of the pseudopotential approach... 

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