Fig. 5: Mechanistic insights into hydrogen bond formation and performance enhancement.

a Differential charge density of TFB-Bth COF. b Differential charge density of Tp-Bth COF (blue, decrease in electron density; yellow, increase in electron density). c DFT calculation of the interlayer binding energy of TFB-Bth COF and Tp-Bth COF. d DFT analysis of torsional energy barriers in single-layer covalent organic frameworks (COFs), with dihedral angles referenced to the central N-N bond within the molecular framework. Both TFB-Bth and Tp-Bth systems exhibit initial torsion angles of −60 °. The horizontal axis represents the torsional angle variation spanning from −60 ° (minimum) to 60 ° (maximum). The figure illustrates the molecular conformations at dihedral angles of −60 °, 0 °, and 60 °. e Interaction energy obtained from DFT calculations and the growth of the COF membranes.