Intuitive and Efficient Approach to Determine the Band Structure of Covalent Organic Frameworks from Their Chemical Constituents

The optical, electronic, and (photo) catalytic properties of covalent organic frameworks (COFs) are largely determined by their electronic structure and, specifically, by their Frontier conduction and valence bands (VBs). In this work, we establish a transparent relationship between the periodic electronic structure of the COFs and the orbital characteristics of their individual molecular building units, a relationship that is challenging to unravel through conventional solid-state calculations. As a demonstration, we applied our method to five COFs with distinct framework topologies. Our approach successfully predicts their first-principles conduction and VBs by expressing them as a linear combination of the Frontier molecular orbitals localized on the COF fragments. We demonstrate that our method allows for the rapid exploration of the impact of chemical modifications on the band structures of COFs, making it highly suitable for further application in the quest to discover new functional materials.

The partitioning between fragments may influence the results and often the best choice is not completely intuitive from the chemical diagram.In the main manuscript we report the results with the closest match with the VASP calculations while in the SI we report alternative partitions.In this table, the best partition for COF-366-Zn, TpPa-1, TP-COF, dual-pore COF, COF-300 and 3D-py-COF presented all are determined by the combination of the localization properties of HOMO and LUMO in dimer rather than the bond distance in the partitioning sites.As powerfully illustrated in Figs.S8-S13, the best partitioning marked in red color effectively separates the frontiers orbitals aside while the blue one almost equally divide these orbitals.Therefore, it is possible to determine the best partition by considering the frontiers orbitals of a dimer composed by the two connected fragments, that is the best partitions have HOMO and LUMO more localized on each of the two portions, such as core and linker in Figs. 1-6 and Figs.S8-S13 (red one)

Figure S1 .
Figure S1.The conduction and valence bands of TP-COF.The CB (a) and VB (b) with the reduced parameters of C 2 L 1 from Fig. 2; the CB (c) and VB (d) with the parameters of C 3 L 1 from another partition from Fig. S8 (blue one); the CB (e) and VB (f) determined from the PBE functional in Gaussian 16.

Figure S2 .
Figure S2.Topological structure with the partitioning core and linker (a) and calculated conduction and valence bands of COF TpPa-1 (hcb) (b).The color in the computed band diagram encodes the fractional contribution of core orbital on the corresponding band.

Figure S3 .
Figure S3.The conduction and valence bands of COF-366-Zn.The CB of the increase orbitals of core (a) and linker (b) from the partitioning in Fig. 3; the CB (c) and VB (d) with the parameters of C 2 L 1 from another partitioning in Fig. S10 (blue one).The color map of band denotes the contribution from the core and linker.

Figure S4 .
Figure S4.The conduction and valence bands of dual-pore COF.The CB of the increase orbitals of core (a) and linker (b) from the partitioning in Fig. 4; the CB (c) and VB (d) with the parameters of C2L1 from another partitioning in Fig. S11 (blue one).The color map of band denotes the contribution from the core and linker.

Figure S5 .
Figure S5.The conduction and valence bands of COF-300.(a) and (b) represent the CB of the increase orbitals of core (C 3 L 1 ) and linker (C 2 L 2 ) from the partition in Fig. 5; (c) and (d) are the CB and VB with the parameters of C 2 L 1 from another partitioning in Fig. S12 (blue one).

Figure S6 .
Figure S6.The conduction and valence bands of 3D-py-COF.he CB of the increase orbitals of core (a) and linker (b) from the partitioning in Fig. 6; the CB (c) and VB (d) with the parameters of C 2 L 1 from another partitioning in Fig. S13 (blue one).The color map of band denotes the contribution from the core and linker.

Figure S7 .
Figure S7.The valence bands (b) of COF-701 from VASP and reduced model with parameter C 2 L 1 from the partitioning core and linker (a), respectively.

Figure S8 .
Figure S8.The different partitioning type of TP-COF.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. 2 while blue one is the alternative partition.

Figure S9 .
Figure S9.The different partitioning type of TpPa-1.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. S2 while blue one is the alternative partition.

Figure S10 .
Figure S10.The different partitioning type of COF-366-Zn.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. 3 while blue one is the alternative partition.

Figure S11 .
Figure S11.The different partitioning type of dual-pore COF.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. 4 while blue one is the alternative partition.

Figure S12 .
Figure S12.The different partitioning type of COF-300.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. 5 while blue one is the alternative partition.

Figure S13 .
Figure S13.The different partitioning type of 3D-py-COF.(a) is the geometrical structure of dimer of connected fragments, (b) is the HOMO and (c) is the LUMO.The red dotted line represents the best partition for the well fitted CB and VB in Fig. 6 while blue one is the alternative partition.

Figure S14 .
Figure S14.Orbitals illustration of (a) 4-member ring and (b) 3-member ring systems.Here cos / are orbital coefficients (not normalised) based on the Hückel theory.sin

Figure S16 .
Figure S16.Projected band structure results for conduction bands of TP-COF using the simplest model with the change of couplings (red in Fig. 2(b)).Colour presents the contribution of  - core orbitals in bands.

Table S2 .
The molecular orbitals information of the partitioning fragments with the good band

Table S4 .
The molecular orbitals information of the partitioning fragments with the good band fitting in COF-300.

Table S5 .
The molecular orbitals information of the partitioning fragments with the good band fitting in 3D-py-COF.

Table S6 .
The molecular orbitals information of the partitioning fragments with the good band

Table S8 .
The consumption of cup-time (hour) of the whole and frontier bands from VASP and optimal parameterized theory model.