Spatial generalizations of Kato's cusp condition for two-electron atoms with correlations

In this work we study two functions, f(r) and g(r), related to spatial generalizations of Kato's cusp condition for the one-electron density. In particular, we evaluate these functions using accurate correlated densities for low-lying S-states of two-electron atoms. These functions reveal the effects of the electron repulsion and are very sensitive to Coulomb correlations, showing interesting features in the comparison between singlet and triplet states. In addition to this, some relationships between and radial expectation values, previously found from the HF properties of these functions, are extended to more accurate descriptions of these states.