The structural complexity of COF-305
COF-305 was synthesized by reacting 20 mg TAM and 17 mg DMTA in 1.25 mL 1,4-dioxane with the presence of 15M acetic acid (HOAc, 200 µL) and aniline (40 µL) at room temperature (Section S2). After 4 days yellowish polyhedral crystals of COF-305 in size of 40 µm were obtained and analyzed by single-crystal X-ray diffraction giving beyond 1 Å resolution. COF-305 crystallized in the space group Fdd2 (No. 43) with unit-cell parameters of a = 47.077(9) Å, b = 67.629(14) Å, c = 42.547(9) Å, α = β = γ = 90º, and V = 135460(47) Å3 (Fig. 2a, Supplymentary Figs. 2–7, Supplymentary Tables 1 and 2). COF-305 is also characterized by solid-state 13C nuclear magnetic resonance, the Fourier-transform infrared, the thermal gravimetric analyses and gas adsorption measurements (Supplymentary Figs. 8–12). High-quality single crystals of COF-304 was crystallized by reacting 2,3-dihydroxyterephthalaldehyde (DHPA) and TAM in a similar condition, having space group of I-4 (No.82), and unit cell parameters a = b = 26.210(6) Å, c = 7.582(3) Å, V = 5208(3) Å3, similar to COF-300 (Fig. 2a, Supplymentary Figs. 13 and 14, and Supplymentary Table 3).
To systematically describe and compare the structure of COF-304 and COF-305, we analyze their structures at three levels, which are struts, diamondoid nets and interpenetration. Here we define the strut as the -Ph-N = C-Ph(X)2-C = N-Ph- (X = H for COF-300, OH for COF-304, OCH3 for COF-305) motif, which is the most basic structural unit. These struts would then link up carbon nodes to form diamondoid nets22, which can be described by the corresponding primitive interpenetration cells (PIC) through translational symmetry operations. PIC can be considered as the minimum primitive crystallographic cell constructed with one of the nets, i.e. the primitive cell to be assigned to the structure if it contains a single network23. The diamondoid nets would then interpenetrate into the voids of each other to give the COF structure, which can be specified by the degree and direction of interpenetration.
For COF-300, half of the -Ph-N = C-Ph-C = N-Ph- strut constitute its crystallographic asymmetric unit, and the diamondoid framework can be described by a simple adamantane cage as the PIC. For COF-304, the -Ph-N = C-Ph(OH)2-C = N-Ph- strut constitutes its crystallographic asymmetric unit (Fig. 2b and Supplementary Fig. 14), and its PIC is also an adamantane cage (Supplymentary Fig. 15). Both COF-300 and COF-304 have 7-fold interpenetration with the vector of [0 0 1], which means each of the interpenetrating networks are offset on the direction of c-axis by one-unit cell length (Supplymentary Fig. 16).
The structure of COF-305, however, is much more complex. The COF has nine different Ph-N = C-Ph(OMe)2-C = N-Ph struts in its asymmetric unit (Fig. 2c, Supplumentary Figs. 3 and 17), which are coded from A to I with different colours. These struts are all in “C” configurations, which is likely due to steric hinderance effect of the methoxy group. The nine struts are stereoisomers and have different length ranging from 18.18 to 18.45 Å (Supplumentary Fig. 18) and their differences in dihedral angles between the imine bond and the benzene rings are shown in Fig. 2c. The PIC of COF-305 is composed of a column of nine corner sharing adamantane cages with one additional strut links to the node of each adamantane cage (Supplumentary Fig. 19). To analyze the structure of PIC more clearly, we only show the adamantane cage without the peripheral struts in Fig. 3a for simplicity. The nine adamantane cages in PIC are coded I to IX according to their sequence along b-axis. The cages can also be labelled by the struts they are made from. For example, cage IV can be marked as F2G4H4I2, indicating that it is composed of two struts F, four struts G, four struts H, and two struts I. In this notation, four pairs of cages have the same compositions, and they could be obtained by symmetry operation (rotating 180º along the c-axis followed by a translation) (Supplumentary Fig. 20). Thus, the nine struts produce five types of non-equivalent cages that constitute the PIC of COF-305 (Supplumentary Fig. 21). It is worth noting that the adamantane cages are more squashed along the stacking direction in COF-305 than COF-300 and 304, indicating the emergence of ordered complexity indeed leverages the complexity of the covalently bonded dia network (Supplumentary Fig. 22). The COF-305 is 5-fold interpenetrated, where five symmetry-equivalent diamondoid networks are related by translation vector [0 1/2 1/2] (Fig. 3b and Supplumentary Fig. 23). The diagonal translation vector of the interpenetration result in different adamantane cages to be placed in the vicinity of each other, giving rise to specific sequences of the nine struts along the b-axis, which is the key structural feature of COF-305 showing its structural complexity.
Viewing along b-axis, the struts show only two types of well-defined sequence, ABCDEFGHI and its reverse, depending on the column of struts being analyzed (Fig. 3c and Supplumentary Fig. 24). In one column, the struts form four pairs, AB, CD, EF, and HI, with struts in each pair having closer distances and curved in opposite directions (Fig. 1b and Supplumentary Fig. 25). The other strut G (labelled orange) is unpaired and more distanced from the adjacent F and H strut. For simplicity, the structural units in the same pair are coded by the same type of colour. The pairing of struts opens void spaces between different pairs, which form channels perpendicular to the packing direction of TAM with the size of 7.3-8.0 Å. These channels are perpendicular to the one-dimensional channel along b-axis, which gives COF-305 three-dimensional porous structure (Supplumentary Fig. 26). In contrast, COF-304, same as COF-300 and other dia COFs, only have one-dimensional channels along the direction of TAM packing (Supplumentary Fig. 27). In summary, COF-305, made from simple building blocks and have simple dia topology, shows structural complexity fundamentally beyond any of the known COFs and the emergence of sequenced linker conformers. The well-defined sequence of these linker conformers on topologically equivalent sites represents a new strategy of COF complexity design, which we would unravel by analyzing the packing geometry and non-covalent interactions associated with DMPA and TAM motif.
The packing geometry of molecular building blocks in COFs and model compounds
The molecular building block packing geometry in COF- 305, along with that of COF-300 and COF-304, is then analyzed to shed light on the origin of its ordered complexity. The TAM building block is known to favour a herringbone packing mode (Supplumentary Table 4 and Supplumentary Fig. 28), which is also a classic synthon in supramolecular chemistry24. Herringbone packing is observed for TAM, tetraphenylmethane (TPM) (Supplumentary Table 5 and Supplumentary Fig. 29), COF-300 and COF-304, but not for COF-305. The key feature of the herringbone packing is the 67° dihedral angles between the interacting benzene rings (Fig. 4a). In COF-300, this 67° dihedral angle is maintained. For COF-304, which has lower symmetry, two dihedral angles of 67° and 62° are found, and the deviation from 67° is associated with the in-plane hydrogen bonding and steric effect involving the hydroxyl groups (Supplumentary Fig. 30). For COF-305, the majority of TAMs are packed in a zigzag mode, which is distinctively different from herringbone packing and have the dihedral angles below 40°. (Fig. 4b and c, and Extended Data Fig. 1f). There is another packing mode of TAMs in COF-305 having two pairs of C-H···C interactions instead of four, which we would name as displaced packing and discuss later (Fig. 4b and Extended Data Fig. 2).
For the packing geometry of aldehyde building blocks, single crystals of the model compounds made by reacting aniline with terephthalic aldehyde, DMPA and DHPA are analyzed, which we refer to as M-300, M-304 and M-305, respectively (Supplumentary Figs. 31–35 and Supplumentary Tables 6–10). It is found that while M-300 and M-304 have phenyl rings in “side-by-side” packing, M-305 has mostly face-to-face packing. In all three COFs, the aldehyde building blocks largely show similar packing mode as their corresponding molecular model compound, with different degree of local deviations (Fig. 4d-f). In summary, COF-300 and 304 have TAM in herringbone packing, aldehyde in “side-by-side” packing, both similar to their corresponding molecular model compounds, whereas COF-305 has TAM in zigzag and displaced packing and the aldehyde in “face-to-face” packing, showing more pronounced difference from the molecular model compounds. In the next section, we would analyze the molecular packing differences between model compounds and COFs in more details and provide a new vision on COF structures from the perspective of molecular assembly that rationalize the emergent of ordered complexity.
Building block packing geometry adaptation and COF structural complexity
For COF-300, both the aldehyde and TAM have minimal deviations from their intrinsically preferred packing, which is evident by the small structural differences between COF-300, TAM and M-300 shown above. The most prominent deviation is the phenyl rings of the terephthalic aldehyde in COF-300 have a slightly larger offset compared to M-300, presumably to accommodate both the preferred herringbone packing of TAM and the imine bonds (Fig. 4d). Thus, the structure of COF-300 can almost be viewed as directly stitching the pre-packed TAM and aldehyde motif through imine bonds. For COF-304, the structural deviations from packing geometry observed in the model compounds are slightly more pronounced due to the hydrogen bonding and steric associated with the OH group, with the dihedral angle of TAM shifted from 67° to 62° and the relative orientation of two imine bonds change from “C” to “S” shape (Fig. 4e, Supplumentary Fig. 36). Comparing COF-300 and 304, it already shows that introducing additional interactions between molecular building blocks can perturb the intrinsically preferred packing more severely and lead to more deviations from these packing modes after COF formation.
For COF-305, stitching TAM in herringbone packing with DMPA would not give a feasible COF structure due to the steric hindrance (Supplumentary Fig. 37), which requires the TAM to adapt to distinctively different zigzag and displaced packing modes. To verify the effect of framework formation on TAM packing, we synthesized another model compound M-305-2 (Supplumentary Table 11, Extended Data Fig. 3, and Supplumentary Figs. 38) from TAM and 2,3-dimethoxybenzaldehyde, where both TAM and dimethoxybenzaldehyde show their intrinsically preferred herringbone and face-to-face packing without the restriction of imine-linked framework. On the other hand, DMPA in COF-305 also shows local slide displacement in three dimensions to accommodate the imine linkage with TAM without dramatically changing the highly preferred face-to-face packing geometry (Supplumentary Table 12). In summary, the ordered complexity in COF-305 is the result of both molecular building blocks deviating from their intrinsically favored simple packing modes to accommodate each other in covalently linked framework.
Based on the observation above, we could propose a postulate for COF synthesis from the perspective of non-covalent interactions. In an ideal case, the molecular building blocks would form the corresponding COF with minimal deviation from their preferred packing geometry and give relatively simple structure in consistent with the simple packing mode of molecular building blocks (e.g. COF-300). However, the topology of the COF requires the molecular building blocks to form covalent bonds with specific connectivity, which in most cases would also require adaptations of the packing geometry of the building blocks considering the steric and other interactions involved in the framework formation. The changes on molecular packing geometry can sometimes be simple and local (e.g. COF-304). However, when simple adaptations are inadequate to accommodate the covalent linkage, as in the case of COF-305, the system would broaden its search in the configuration space and result in each building block to pack in less favorable modes, which could give a series of configurations that coexist and result in structural complexity (Extended Data Fig. 1e). Such rationalization can be supported by quantitative analysis of the interacting struts in COF-305, where the rich library of stereoisomers readily embodies the gradual deviation from preferred packing modes that is locally more energetically favorable.
Energy calculation of the nine pairs of interacting struts in COF-305 quantitatively shows how molecular building blocks make compromises in their packing geometry to accommodate each other in the framework (Fig. 5, and Supplumentary Table 12). The energy of the interacting struts is mainly affected by two factors: the packing mode of TAM and the lateral offset value of DMPA. For TAM, calculation shows the zigzag mode is energetically more favorable than displaced packing: the GH struts with displaced packing on both sides shows highest energy, and the FG and HI struts having displaced packing on one side show the second and third highest energy. For the other six pairs of struts with all zigzag TAM packing, the offset value of DMPA determines their energy. M-305 represents the intrinsically favored packing of DMPA, and more deviation from this structure gives higher energy, which is evident by the correlation between energy and the lateral offset value between DMPA (Fig. 5c). In other words, in COF-305, only part of the DMPA can stay in its intrinsically preferred packing mode, while the others much adapt different packing geometry to give structural complexity. On the other hand, it can also be inferred that having molecular building blocks deviating from their preferred packing could also lead to geometries too unfavorable for COF formation and result in defects or even failure in crystallization. We believe this could be the reason for poor crystallinity of many COFs, and further building block design based on consideration on molecular packing would greatly increase the COFs with high crystallinity and complex structures.