First principles study of [111]-oriented epitaxially strained rare-earth nickelate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>NdNiO</mml:mi> <mml:mn>3</mml:mn> </mml:msub> </mml:math>

Density functional theory is used to investigate the effect of biaxial strain on the structural, electronic and magnetic properties of [111]-oriented <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:msub> <a:mi>NdNiO</a:mi> <a:mn>3</a:mn> </a:msub> </a:math> , as a representative of the rare-earth perovskites that undergo metal-to-insulator transitions. We find that this constraint on the system induces unique structural phase transitions not previously observed under the well-studied bulk or [001]-oriented strained systems. We also report unique electronic behavior, including amplification of the electronic band gap with tensile strain, and insulating, charge-ordered phases with nonorthorhombic tilt patterns. To provide clarity to the trends we observe, we also investigate the coupling between the breathing mode and strain, where we observe certain strains to directly favor and disfavor the creation of the breathing mode (and thus the associated charge-ordering). The amplification of the band gap with strain is understood in terms of a cooperative coupling between the elastic constraint and octahedral breathing, which expands on the previously reported triggered mechanism mediated by octahedral tilting.