  Superconductivity is one of the most intriguing properties of matter
described by an attractive interaction that bounds electrons into Cooper pairs.
To date, the highest critical temperature at ambient conditions is achieved in
copper oxides. While layered nickel oxides were long proposed to be analogous
to cuprates, superconductivity was only demonstrated in 2019 albeit without
clarifying the pairing mechanism. Here we use Density Functional Theory (DFT)
to show that superconductivity in nickelates is driven by an electron-phonon
coupling originating from a charge ordering. Due to an intrinsic electronic
instability in half-doped compounds, Ni$^{1.5+}$ cations dismutate into more
stable Ni$^+$ and Ni$^{2+}$ cations, which is accompanied by a bond
disproportionation of NiO$_4$ complexes producing an insulating charge ordered
state. Once doping suppresses the instability, the bond disproportionation
vibration is sufficient to reproduce the key characteristic of nickelates
observed experimentally, notably the dome of T$_c$ as a function of doping
content. These phenomena are identified if relevant degrees of freedom as well
as an exchange correlation functional that sufficiently amends self-interaction
errors are involved in the simulations. Finally, despite the presence of
correlation effects inherent to $3d$ elements, nickelates superconductors
appear similar to non-magnetic bismuth oxide superconductors.
