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Covalent organic frameworks (COFs) offer a high degree of chemical andstructural flexibility. There is a large family of COFs built from 2D sheetsthat are stacked to form extended crystals. While it has been common torepresent the stacking as eclipsed with one repeating layer ("AA"), there isgrowing evidence that a more diverse range of stacking sequences is accessible.Herein, we report a computational study of layer stacking in two prototypicalCOFs, Tp-Azo and DAAQ-TFP, which have shown high performance as Li-ion batteryelectrodes. We find a striking preference for slipped structures withhorizontal offsets between layers ranging from 1.7 \r{A} to 3.5 \r{A} in apotential energy minimum that forms a low energy ring. The associated symmetrybreaking results in a pronounced change in the underlying electronic structure.A band gap opening of 0.8 - 1.4 eV is found due to modifications of theunderlying valence and conduction band dispersion as explained from changes inthe $\pi$ orbital overlap. The implications for the screening and selection ofCOF for energy applications are discussed.

Band gap opening from displacive instabilities in layered covalent-organic frameworks $^\dag$