We use first-principles calculations to find that in infinite-layer nickelates RNiO 2 , the widely studied tetragonal P 4/mmm structure is only dynamically stable for early lanthanide elements R = La-Sm. For late lanthanide elements R = Eu-Lu, an imaginary phonon frequency appears at A = (π, π, π) point. For those infinite-layer nickelates, condensation of this phonon mode into the P 4/mmm structure leads to a more energetically favorable I4/mcm structure that is characterized by an out-of-phase rotation of "NiO 4 square". Special attention is given to two borderline cases: PmNiO 2 and SmNiO 2 , in which both the P 4/mmm structure and the I4/mcm structure are local minimums, and the energy difference between the two structures can be fine-tuned by epitaxial strain. Compared to the P 4/mmm structure, RNiO 2 in the I4/mcm structure has a substantially reduced Ni d x 2 −y 2 bandwidth, a smaller Ni d occupancy, a "cleaner" Fermi surface with less contribution from lanthanide element d orbitals, and a decreased critical U Ni to stabilize long-range antiferromagnetic ordering. All these features favor Mott physics and render RNiO 2 in the I4/mcm structure a closer analogy to superconducting infinite-layer cuprates.