We present an effective two-band model for infinite-layer nickelates ${\mathrm{NdNiO}}_2$ that consists of a $d$ band centered at the Ni site and an interstitial $s$-like band centered at the Nd site. To the large extent of the wave functions, we find intersite Coulomb interactions to be substantial. We then use the variational cluster approach together with mean-field theory to investigate magnetic and charge ordering. While tendencies towards charge modulation are found, they are weak and might be due to finite-size effects. Magnetic order is determined mostly by the filling of the $d$ band and hardly affected by including longer-ranged interactions. For a $d$-band density consistent with density-functional theory, magnetic ordering vanishes once quantum fluctuations are included to a sufficient spatial extent. Apart from self-doping, $d$ and $s$ bands remain largely uncoupled despite the presence of interorbital Coulomb interaction and (small) interorbital hopping.

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• Charge density waves
• First-principles calculations
• Magnetic order
• Superconductivity
• Nickelates