In the right hand side (RHS) of Eqs. ( ) and (4), the subscript 1 from the coordinates of the reference electron is dropped, i.e. σ 1 = σ and r 1 = r, a notation that will be kept for the rest of the paper. The functions χ m and Φ m in Eq. ( ) are called marginal and conditional amplitude, respectively, and are constrained by the so-called partial normalization condition (PNC):