  High temperature superconductivity has been found in many kinds of compounds
built from planes of Cu and O, separated by spacer layers. Understanding why
critical temperatures are so high has been the subject of numerous
investigations and extensive controversy. To realize high temperature
superconductivity, parent compounds are either hole-doped, such as
{La$_{2}$CuO$_4$} (LCO) with Sr (LSCO), or electron doped, such as
{Nd$_{2}$CuO$_4$} (NCO) with Ce (NCCO). In the electron doped cuprates, the
antiferromagnetic phase is much more robust than the superconducting phase.
However, it was recently found that the reduction of residual out-of-plane
apical oxygens dramatically affects the phase diagram, driving those compounds
to a superconducting phase. Here we use a recently developed first principles
method to explore how displacement of the apical oxygen (A-O) in LCO affects
the optical gap, spin and charge susceptibilities, and superconducting order
parameter. By combining quasiparticle self-consistent GW (QS\emph{GW}) and
dynamical mean field theory (DMFT), that LCO is a Mott insulator; but small
displacements of the apical oxygens drive the compound to a metallic state
through a localization/delocalization transition, with a concomitant maximum
$d$-wave order parameter at the transition. We address the question whether NCO
can be seen as the limit of LCO with large apical displacements, and elucidate
the deep physical reasons why the behaviour of NCO is so different than the
hole doped materials. We shed new light on the recent correlation observed
between T$_c$ and the charge transfer gap, while also providing a guide towards
the design of optimized high-Tc superconductors. Further our results suggest
that strong correlation, enough to induce Mott gap, may not be a prerequisite
for high-Tc superconductivity.
