PSEUDOPOTENTIAL METHODS AND VALENCE APPROXIMATION

The very first formulation of the pseudopotential idea is almost as old as quantum chemistry itself. It belongs to Hans Hellmann [32-35] who proposed to use the potential energy for an electron in the valence shell of an atom in the form  

Although historically pseudopotentials appear in numerous disguises on which we do not dwell here, the modem derivation of the pseudopotential theory [36] is based 

Up to this point nothing changes. The next assumption extends the above treatment of atoms to molecules. Within it the molecular orbitals - linear combinations of the atomic core orbitals with zero overlap - are taken to be the molecular core orbitals and are assumed to be filled. This allows one to write 

It can be shown that the Huzinaga-Cantu equation, and thus the MP setting, can be used for molecules, provided a reasonable approximation for the core orbitals is known. It is normally true, as the concept of the atomic core is multiply confirmed by all electron calculations on smaller molecules and there is no reason to think that this picture will change in the case of larger ones. 

Since in current molecular modeling tasks the Gaussian orbitals or their linear combinations are used, one can guess that they provide the explicit form of the core states. Inserting the Gaussians in the expressions for the Coulomb and exchange superoperators yields numerous approximate forms of the pseudopotentials, which can be exemplified by the formulae employed in the ab initio model potential (AIMP) [36]  

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