  In this paper we investigate the electronic and superconducting properties in
nickelate compounds of NiO2 through Perturbative Density Functional Theory
(P-DFT) and multi-band BCS theory. We consider three different cases of study
(i) the crystalline structure composed by two layers of NiO2, with a central
single atom of Nd, Yb or Pr, which is subjected to mechanical compression and
tension forces (pressure), (ii) the crystalline structure composed by three
layers of NiO2 with central atom pairs of Nd-Nd, Nd-Sr or Sr-Sr, where the
level doping x correspond to change between Nd/Sr and (iii) through multi-band
theory we study the behaviour in a single-layer Nd1-xSrxNiO2} when $x$=0.5
through gaps $\Delta_{\chi,\textbf{p}}$, with $\chi$ (number of band or
orbitals), only with the presence of inter-band coupling $V_{\chi\chi'}$. As
results, for (i) and (ii) we present the electronic measures of the electronic
band structures \textit{e-DOS}, \textit{p-DOS}. In (i) we show that under
pressure there are a re-distribution of the band structures for \textit{e-DOS},
\textit{p-DOS}, allowing the destruction of van-\textit{Hove} near Fermi level
$E_{F}$, thus in (ii) we show the presence of a single flat band when the
doping level is $x$=0.5 and for (iii) the inter-band coupling between orbitals
play a key role in the construction of a superconducting phase in nickelates
compounds.
