Pseudopotentials generalized Philips-Kleinman

The term in the square brackets is the generalized Philips-Kleinman pseudopotential, yGPK... 

Since the core spinors are eigenfunctions of /, the generalized Philips-Kleinman pseudopotential can be written... 

We would also like to partition the Fock operator into a valence and a core part this we will do later. In the rest of this section, we explore the development of the generalized Philips-Kleinman pseudopotential for many valence electrons and many valence spinors. 

The generalized Philips-Kleinman pseudopotential depends on the eigenvalue of the spinor v, unlike the frozen-core pseudopotential, which depends only on the core spinors. The appearance of the term in the pseudopotential came about because we transferred a term from right-hand side of (20.21). This means that we have changed the metric, which has implications for orthogonality that we pursue later. The new operator makes the core spinors degenerate with the valence spinor ... 

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