Recasting of correlated wavefunctions in helium ground state

5 Recasting of correlated wavefunctions in helium (ground state) 

As implied by the name, a correlated wavefunction takes into account at least some essential parts of the correlated motion between the electrons which results from their mutual Coulomb interaction. As analysed in Section 1.1.2 for the simplest correlated wavefunction, the helium ground-state function, this correlation imposes a certain spatial structure on the correlated function. In the discussion given there, two correlated functions were selected a three-parameter Hylleraas function, and a simple Cl function. In this section, these two functions will be represented in slightly different forms in order to make their similarities and differences more transparent. 

When applying the Cl model to the ground state of helium, the 2p2 S basis function makes a significant contribution, and the expansion 

From equ. (7.102) it can be inferred that no spatial structure is imposed on the electrons, i.e., no correlation effects are included. 

Similarly, one can calculate the two-electron basis functions contained in equ. 

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