Structural stability, electronic structure, and magnetic properties of the single-layer trilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>La</mml:mi> <mml:mn>3</mml:mn> </mml:msub> <mml:msub> <mml:mi>Ni</mml:mi> <m

A polymorph of the bilayer nickelate La3Ni2O7 that displays an alternating single-layer (SL) and trilayer (TL; 1313) stacking pattern has recently been discovered. Signatures of superconductivity under pressure have been found in this phase. At ambient pressure, La3Ni2O7-1313 has been reported to crystallize in three different space-group symmetries Cmmm, Imma, and Fmmm. Unlike the commonly observed tilted NiO6 octahedra in perovskite nickelates, the Cmmm phase exhibits no NiO6 tilts, implying that this structural feature alone may be insufficient to give rise to superconductivity in Ruddlesden-Popper nickelates. Here, we employ first-principles calculations and group theory analysis to study the pressure dependence of the structural instabilities in this SL-TL La3Ni2O7 polymorph. At ambient pressure, we identify multiple unstable phonon branches in the highest symmetry (Cmmm) structure at various high-symmetry points of the Brillouin zone. Distortions associated with these instabilities lead to one of the other experimentally reported space groups (Imma) that does display octahedral tilts. The magnetic tendencies indicate that the electronic structure of La3Ni2O7-1313 at ambient pressure is dominated by the TL block, as the SL is in a Mott-insulating regime. Under pressure, a tetragonal P4/mmm structure becomes stable, in agreement with experiments.