Huzinaga-Cantu equation

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. 

Effective Core Potential methods are classified in two families, according to their basic grounds. On the one hand, the Pseudopotential methods (PP) rely on an orbital transformation called the pseudoorbital transformation and they are ultimately related to the Phillips-Kleinman equation [2]. On the other hand, the Model Potential methods (MP) do not rely on any pseudoorbital transformation and they are ultimately related to the Huzinaga-Cantu equation [3,4]. The Ab Initio Model Potential method (AIMP) belongs to the latter family and it has as a... 

The equation that is used to ensure that the core spinors are projected out is the Huzinaga-Cantu equation (Huzinaga and Cantu 1971, Huzinaga et al. 1973), which we will now derive. Instead of writing the Fock equations for the valence spinors in terms of Lagrange multipliers and imposing the criterion that the overlaps must be zero at convergence, we can introduce projection operators into the Fock operator ... 

This is the Huzinaga-Cantu equation. It has similar properties to (20.91), but instead of fkv being indeterminate it is zero. The projector term in the Fock operator functions as a level shift core spinors are moved up by 2 q. The advantage of this is that there is an energetic cost for any core spinors that come from other centers to mix into the valence spinors, and therefore the mixing is not likely. We will return to this point later. 

Explicit orthogonality constraints can be removed by transforming the hamiltonian so that it only acts on a specific subspace (e.g. the valence space) of the all-electron space. This can be done formally by the use of the projection operator method (see Huzinaga and Cantu or Kahn, Baybutt, and Truhlar "). If the core function is written as in equation (6) a projection operator may be defined for each valence electron /i ... 

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