  The Schroedinger equation for two electrons in the field of a charged fixed
center $Z$ is solved with the Lagrange mesh method for charges close to the
critical charge $Z_{cr}$. We confirm the value of the nuclear critical charge
$Z_{cr}$ recently calculated in Estienne et al. {\em Phys. Rev. Lett. \bf 112},
173001 (2014) to 11 decimal digits using an inhomogeneous (non-uniform)
three-dimensional lattice of size $70 \times 70 \times 20$. We show that the
ground state energy for H$^-$ is accurate to 14 decimals on the lattice $50
\times 50 \times 40$ in comparison with the highly accurate result by
Nakashima-Nakatsuji, {\it J. Chem. Phys. \bf 127}, 224104 (2007).
