To find an ansatz for the correlated part of the wave function, it is useful to rewrite the two-particle local energy in terms of the relative and center-of-mass motion. Let us denote the distance between the two electrons as r_{12} . We omit the center-of-mass motion since we are only interested in the case when r_{12} \rightarrow 0 . The contribution from the center-of-mass (CoM) variable \boldsymbol{R}_{\mathrm{CoM}} gives only a finite contribution. We focus only on the terms that are relevant for r_{12} and for three dimensions. The relevant local energy becomes then \lim_{r_{12} \rightarrow 0}E_L(R)= \frac{1}{{\cal R}_T(r_{12})}\left(2\frac{d^2}{dr_{ij}^2}+\frac{4}{r_{ij}}\frac{d}{dr_{ij}}+ \frac{2}{r_{ij}}-\frac{l(l+1)}{r_{ij}^2}+2E \right){\cal R}_T(r_{12}) = 0. Set l=0 and we have the so-called cusp condition \frac{d {\cal R}_T(r_{12})}{dr_{12}} = -\frac{1}{2(l+1)} {\cal R}_T(r_{12})\qquad r_{12}\to 0