Correlation effects close to the ground state critical charge of the two-electron atom

Abstract

The critical charge, at which the “first ionization energy” of the ground-state of the two-electron atom vanishes, is evaluated for the radial limit, as well as for the s+p,s+p+d,s+p+d+f and s+p+d+f+g partially angularly correlated variational limits, getting closer and closer to the fully-correlated critical charge. The (counterintuitive) square integrability of the various correlated wave functions at their respective critical charges is deduced by noting that the derivatives of the corresponding binding energies with respect to Z (hence, the expectation values of the interelectronic repulsion) remain non-vanishing upon approaching these critical nuclear charges.