Basis sets and related concepts

All of the electronic structure methods described above make use of basis sets. This is because the corresponding HF, Cl, or Kohn-Sham equations cannot be solved analytically. The solution to this problem was first given by Roothaan80 who suggested expanding the orbitals in terms of a known 

The problem of inner electrons does not only affect plane wave periodic calculations. In cluster calculations, inner, or core electrons, are also often replaced by pseudopotentials to reduce the computational effort. This reduction of the number of active electrons simplifies and shortens the 

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