Methods Involving the Interelectronic Distance

The necessity of going beyond the HF approximation is due to the fact that electrons are further apart than described by the product of their orbital densities, i.e. their motions are correlated. This arises from the electron-electron repulsion operator, which is a sum of terms of the type shown in eq. (4.73). 

Without these terms, the Schrodinger equation can be solved exactly, with the solution being a Slater determinant composed of orbitals. 

The electron-electron repulsion operator has a singularity for = 0 which results in the exact wave function having a cusp (discontinuous derivative), since the kinetic energy must cancel the infinity of the potential energy to give a finite result. 

The cusp condition imphes that the exact wave function must be Hnear in the interelectronic distance for small values of ri2. 

It would therefore seem natural that the interelectronic distance should be a necessary variable for describing electron correlation. For two-electron systems, extremely 

---