Pseudopotentials and atomic operators

The basic idea behind the pseudopotential method is to treat the valence electron as moving in a potential from a fixed ion core. Chemically this is very reasonable and it is only if one is interested in very accurate investigation of spectroscopic data of elements with highly polarizable cores (typically alkali metals) that this approach fails7. 

The Fock operator defined in eq. (2.7) above, here rewritten for a closed shell system, can be diagonalized and expressed in terms of the core (c) valence (v) and excited state (e) projectors as7  

The valence pseudo-Fock operator takes the form  

The pseudopotential, FPS, may be derived by minimizing the distance between/ and either the full Fock operator, i.e, H/P5 — / min. or the truncated valence Fock-like operator, /ps min, where 

However, this is definitely the technique for future calculations involving a large number of metal atoms. Furthermore, the idea behind the pseudopotential method is also applied in other types of Hamiltonians described below, e.g., valence effective Hamiltonian and semi-empirical methods. 

---