ABSTRACT
This chapter explains the two-electron systems. This includes not only helium and helium-like systems, but also systems where the first approximation is modelled as a core and two valence electrons such as beryllium and magnesium. These are the simplest systems in which the correlation is studied but many interesting challenges and examples of complex problems are exhibited. The chapter further states that many general methods are applied to the helium-like systems. In MCHF calculations, it is usually advisable to start with a Hartree-Fock calculation for the dominant term in the expansion and then add new orbitals to the calculation. There are basically two different ways of increasing the set of orbitals in a systematic way, for a reduced pair expansion. The simplicity of the MCHF method makes it well suited to the fairly accurate calculations for lowly excited states of two-electron systems, but its real strength is more apparent for other cases.
