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for LNO on both LAO and STO which indicates excellent accuracy between the two structure determination methods. We note that the DFT ground state indicates an additional energy lowering distortion through small antiparallel displacements of ∼ 0 . 01 ˚ A for the La atoms along the [110] directions. Such displacements would produce weak but measurable ( 1 / 2 1 / 2 1 / 2 ) and ( 3 / 2 3 / 2 3 / 2 ) peaks, which however were not observed in the diffraction measurements, and likely persists in the DFT calculations due to the common exchange-correlation functional underestimation of the equilibrium volume. 

