  Covalent organic frameworks (COFs) offer a high degree of chemical and
structural flexibility. There is a large family of COFs built from 2D sheets
that are stacked to form extended crystals. While it has been common to
represent the stacking as eclipsed with one repeating layer ("AA"), there is
growing evidence that a more diverse range of stacking sequences is accessible.
Herein, we report a computational study of layer stacking in two prototypical
COFs, Tp-Azo and DAAQ-TFP, which have shown high performance as Li-ion battery
electrodes. We find a striking preference for slipped structures with
horizontal offsets between layers ranging from 1.7 \r{A} to 3.5 \r{A} in a
potential energy minimum that forms a low energy ring. The associated symmetry
breaking 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 the
underlying valence and conduction band dispersion as explained from changes in
the $\pi$ orbital overlap. The implications for the screening and selection of
COF for energy applications are discussed.
