Stereoselective gridization and polygridization with centrosymmetric molecular packing

The gridarenes, with well-defined edges and vertices, represent versatile nanoscale building blocks for the installation of frameworks and architectures but suffer from difficulty in stereoselective control during their synthesis. Here we report a diastereoselective gridization of superelectrophilic diazafluorene-containing substrates (AmBn) with crescent shapes into Drawing Hands grids (DHGs). The meso-selectivity reaches 75.6% diastereomeric excess (de) during the gridization of A1B1-type substrates and maintains ~80% de during the polygridization of A2B2-type monomers. Such stereocontrol originates from the centrosymmetric molecular packing of two charge-delocalized superelectrophiles with synergistically π–π stacking attractions and coulombic repulsions. As meso-stereoregular structures show 20∼30 nm in length, the rigid ring/chain-alternating polygrids have a Mark–Houwink exponent of 1.651 and a molecular weight (M) dependence of the hydrodynamic radius Rh ∼ M1.13. Via the simulation of chain collapse, meso-configured polygridarenes still adopt rod-like conformations that facilitate the high rigidity of organic nanopolymers, distinguished from toroid backbones of rac-type polygrids.

to reflux for 20 min. It is noted that the Grignard reagent should be dropped very slowly. Then NH4Cl solution was added to quench and neutralize the reaction. Then DCM was added for extraction, and the aqueous layer was washed by DCM for three times. The combined organic solution was dried with anhydrous Na2SO4. After the filtration, the crude product was collected by evaporating the solvent. The crude product was purified by column chromatography [silica gel, petroleum ether: DCM: ethyl acetate = 2:2:1, trimethylamine (2 drops per 100 ml eluent) should be added in whole isolation] and washing with petroleum ether and DCM to give 1c (White solid, 494 mg, 1.34 mmol. Yield: 67%). It is noted that higher temperature (30~40 o C) can lead to byproducts, which reduces the yield of 1c. 1

meso-DHG1
White solid, 97 mg, 0.   MC2 (140 mg, 0.3 mmol, 1 equiv) was added in 22.5 ml DCM solvent and 7.5 ml CF3COOH mixed solvents and then the solution was stirred (under 20 o C). Then CF3SO3H (2 ml, 22.8 mmol, 75 equiv) were added quickly. After the reagent MC2 was completely consumed (in 1 minute) as monitored by TLC, the excessive solution of potassium hydroxide was added very slowly at the temperature of 0 o C and then extracted with DCM. The mixed organic phase was dried over anhydrous Na2SO4 and then this organic phase was filtered and concentrated under low pressure. The crude product was purified by column chromatography [silica gel, trimethylamine (2 drops per 100 ml eluent) should be added in whole isolation] to give meso-DHG2 (Eluent: DCM: ethyl acetate = 2:1), rac-DHG2 (Eluent: DCM: ethyl acetate = 2:1) and the byproducts MG2 (oligomer cycles, a series of homolog, Eluent: DCM: methyl alcohol = 10:1). It is noted that no linear irregular oligomers were observed.

MC3
(170 mg, 0.3 mol, 1 equiv) was added in 20 ml DCM solvent and 7 ml CF3COOH mixed solvents and then the solution was stirred (under 20 o C). Then CF3SO3H (2 ml, 22.8 mmol, 75 equiv) were added quickly. After the reagent MC3 was completely consumed (in 1 minute) as monitored by TLC, the excessive solution of potassium hydroxide was added very slowly at the temperature of 0 o C and then extracted with DCM. The mixed organic phase was dried over anhydrous Na2SO4 and then the organic phase was filtered and concentrated under low pressure. The crude product was purified by column chromatography [silica gel, trimethylamine (2 drops per 100 ml eluent) should be added in whole isolation] to give meso-DHG3 (Eluent: DCM: ethyl acetate = 3:1), rac-DHG3 (Eluent: DCM: ethyl acetate = 2:1) and the byproducts MG3 (oligomer cycles, a series of homolog, Eluent: DCM: methyl alcohol = 10:1).

MC4
(200 mg, 0.23 mmol, 1 equiv) was added in 15 ml DCM solvent and 5 ml CF3COOH mixed solvents and then the solution was stirred (under 20 o C). Then CF3SO3H (1.5 ml, 17.5 mmol, 75 equiv) were added quickly. After the reagent MC4 was completely consumed (in 1 minute) as monitored by TLC, the excessive solution of potassium hydroxide was added very slowly at the temperature of 0 o C and then extracted with DCM. The mixed organic phase was dried over anhydrous Na2SO4 and then the organic phase was filtered and concentrated under low pressure. The crude product was purified by column chromatography [silica gel, trimethylamine (2 drops per 100 ml eluent) should be added in whole isolation] to give meso-DHG4 (Eluent: petroleum ether: DCM: ethyl acetate = 5:5:1.), rac-DHG4 (Eluent: petroleum ether: DCM: ethyl acetate = 2:2:1) and the byproducts MG4 (oligomer cycles, a series of homolog, Eluent: DCM: methyl alcohol = 10:1). Even so, the product rac-DHG4 is impure and they are mixed with MG4. As a result, we further isolated them via HPLC.

meso-DHG4
Yellow  MC5 (200 mg, 0.2 mmol, 1 equiv) was added in 15 ml DCM solvent and 5 ml CF3COOH mixed solvents and then the solution was stirred (under 20 o C). Then CF3SO3H (1.3 ml, 15 mmol, 75 equiv) were added quickly. After the reagent MC5 was completely consumed (1 minute) as monitored by TLC, the excessive solution of potassium hydroxide was added very slowly at the temperature of 0 o C and then extracted with DCM. The mixed organic phase was dried over anhydrous Na2SO4 and then the organic phase was filtered and concentrated under low pressure. The crude product was purified by column chromatography [silica gel, trimethylamine (2 drops per 100 ml eluent) should be added in whole isolation] to give meso-DHG5 (Eluent: petroleum ether: DCM: ethyl acetate = 5:5:1.), rac-DHG5 (Eluent: petroleum ether: DCM: ethyl acetate = 2:2:1, but it was evidently mixed with other macrocyclic byproduct, thus we did not obtained its NMR spectra. The yield is roughly evaluated to be 4%) and the byproducts MG5 (oligomer cycles, a series of homolog, Eluent: DCM: methyl alcohol = 10:1). It is noted that no linear irregular oligomers were observed.

Nano-linkage by polygridization
DC-F (52 mg, 0.04 mmol, 1 equiv) was added in 1.5 ml DCM and 0.5 ml TFA solvent, then the solution was stirred (under 20 o C). Then CF3SO3H (0.40 ml, 4.55 mmol, 114 equiv) were added quickly. 6~25 seconds later, we added MC1 (5~10 mg, 0.01~0.021 mmol, 0.26~0.52 equiv) quickly to terminate the intermediates. Then in 1 min, the excessive solution of potassium hydroxide was added slowly at the temperature of 0 o C and then extracted with DCM. It is noted that the solvent should be added in less amount (high concentration of DC-F) to ensure the instantly complete contact between polymeric intermediates and MC1, which determining the success of this polygridization. In addition, adding the highly excessive amount of MC1 (2 equiv of DC-F monomers) leads to introducing the byproduct MG1 derived from MC1 end-capping reagent. The mixed organic phase was dried over anhydrous Na2SO4 before organic phase was filtered and concentrated under low pressure. After filtration the crude product was collected by evaporating the solvent. The crude product was purified by Soxhlet extraction using tetrahydrofuran and acetone mixing solvents.  1438, 1374, 1350, 1294, 1249, 1215, 1179, 1157, 1129, 1032, 880, 815, 804, 749, 702, 694, 634, 621. It is noted that the integration in the spectrum only represented the integration ratio rather than the fact number of hydrogen atoms.

Theoretical calculations and simulations Method for the vibrational simulation of meso-DHG1 and rac-DHG1
The simulation method of vibration modes of DHG1 backbones was detailed. For both meso-DHG1 and rac-DHG1, the geometric optimization was performed under the calculation method of RB3LYP and the basis set of 6-31G (D). On this basis, the vibrational simulation was performed under the method of RB3LYP and the basic set of 6-31G(D). The scaling factor 0.9614 is referred to the literature 4 . The output files for meso-DHG1 and rac-DHG1 are provided as the Supplementary Data 1 and 2 respectively.

The calculation of cohesive energy density of PDHG-F chains.
The amorphous structure consisting of 5 chains of PDHG-F (each chain exhibits the DP of 9, approximate to the experimental results) was constructed via the "Amorphous cell" modules in the Material Studio 2016 software. The initial density is set as 0.2 g cm -3 . Then, the geometry optimization (in Forcite plus modules) was carried out based on the SMART algorithum (that is the cascade algorithum of the Steepest Descent, ABNR and Quasi-Newton methods, in sequence), an energy convergence tolerance of 0.0001 kcal mol -1 , a force convergence tolerance of 0.005 kcal mol -1 Å -1 , the maxium number of iterations of 200000. In addition, we used COMPASS force field 5 in which the summation method of Electrostatic terms was set as the Ewald (a buffer width of 0.5 Å) and the summation method of van der Waals terms was used as the Group based (a cutoff distance of 15.5 Å). The MD simulation after the geometry optimization was firstly performed via the Forcite plus modules based on the NPT ensemble, 298 K, 10 -4 GPa, a total time of 1100 ps with a time step of 1.5 fs, COMPASS force field, Group-based summation of van de Waals terms (cutoff: 15.5 Å) and Ewaldsummation of electrostatic terms. In order to obtain the statistic conformations in equilibrium state, then we carried out the NVT dynamics based on the 298 K, a total simulation time of 3000 ps with a time step of 1.5 fs. The actual conformational state was obtained every 5000 steps. For each conformations, we calculated the cohesive energy density (CED) using the equation CED = Einter / V, where Einter is defined as the total energy of intermolecular interactions (in this case, the intermolecular attractive force should be stronger than intermolecular repulsion) and V is equal to the volume of amorphous cell. The cohesive energy density table of PDHG-F chains is provided as the Supplementary Data 3.

The calculation of cohesive energy density of CHCl3 solvent.
We constructed the amorphous structures of CHCl3 solvent molecules via the "Amorphous cell" modules (the density was set as the 1.48 g cm -3 that is the consistent with the real density, and the number of CHCl3 molecules was set as 30). Then, such system was subjected to the NVT ensemble based on the 298 K, a total time of 600 ps with a time step of 1.5 fs, COMPASS force field, Group-based summation of van de Waals terms (cutoff: 15.5 Å) and Ewald-summation of electrostatic terms. The actual conformation during the 300~600 ps of the dynamic procedure was saved every 4000 steps to calculate the cohesive energy density using the equation CED = Einter / V, where Einter is defined as the total energy of intermolecular interactions (in this case, the intermolecular attractive force should be stronger than intermolecular repulsion) and V is equal to the volume of amorphous cell. The cohesive energy density table of CHCl3 solvent is provided as the Supplementary Data 4.

The calculation of cohesive energy density of tetrahydrofuran solvent.
The amorphous structures of tetrahydrofuran solvent molecules was constructed via the "Amorphous cell" modules (the density was set as the 0.89 g cm -3 that is the consistent with the real density, and the number of tetrahydrofuran molecules was set as 30). Then, such system was subjected to the NVT ensemble based on the 298 K, a total time of 600 ps with a time step of 1.5 fs, COMPASS force field, Group-based summation of van de Waals terms (cutoff: 15.5 Å) and Ewald-summation of electrostatic terms. The actual conformation during the 300~600 ps of the dynamic procedure was saved every 4000 steps to calculate the cohesive energy density using the equation CED = Einter / V, where Einter is defined as the total energy of intermolecular interactions (in this case, the intermolecular attractive force should be stronger than intermolecular repulsion) and V is equal to the volume of amorphous cell. The cohesive energy density table of tetrahydrofuran solvent is provided as the Supplementary Data 5. -F (full rac-configurational PDHG-F chains).

The chain collapse simulation of meso-PDHG-F (full meso-configurational PDHG-F chains) and rac-PDHG
The simulation of chain collapse for other chain length such as DP = 7, 9 and 18 were detailed. All PDHG-F chains were constructed in the expanded conformations where the dihedral angle between adjacent repeat units are approximate to 180 o . The dynamics of chain collapse were carried out under the conditions of NVT ensemble (298 K) and the COMPASS forcefield (the summation method of van de Waals term and the electrostatic term are both Group-based in which the cutoff distance were set as 12.5 Å). For DP = 7, the total times of dynamics were set as 600 ps for meso-PDHG-F with the time step of 1.5 ps. For rac-PDHG-F (DP = 7), the total times of dynamics were set as 2000 ps with the time step of 1.5 ps. For DP = 9, the total times of dynamics were set as 500 ps for meso-PDHG-F with the time step of 1.5 ps. For rac-PDHG-F (DP = 9), the total times of dynamics were set as 500 ps with the time step of 1.5 ps. For DP = 18, the total times of dynamics were set as 800 ps for meso-PDHG-F with the time step of 1.5 ps.  Supplementary Figure 12. The FT-IR spectra of the doping systems where meso-DHG1 and rac-DHG1 are mixed in specific ratio (0% de = 1:1 of meso-DHG1: rac-DHG1; 33% de = 2:1; 50% de = 3:1; 60% de = 4:1; 67% de = 5:1). The red region ranges from 1294 to 1248 cm -1 , which exhibits stronger band intensity in meso-DHGs. The green region exhibits the band at 1100~1085 cm -1 , which is more powerful in rac-DHGs. The blue region includes the vibrational absorption at 1030~1024 cm -1 , which is stronger in rac-DHGs.

Supplementary Note 4. The calculation of expansion factor β of PDHG-F in solution
To testify the validity of stereoselective demonstration relying on c/i/N8 signals, we studied the chain conformation of PDHG-F via the molecular dynamic simulation. For the relatively good solvent CHCl3, the solvent molecules enable to interact with the PDHG-F chain and amplify the excluded volume effect to expand the chain backbones. To demonstrate such point, we referred to the equation ES1 8 : C(1/xs -2χ)N 1/2 = β 5β 3 , where C is the length ratio of the repeat units to Kuhn segments (defined as the equivalent chains that consist of rigid segments via the linkage of flexible covalent bonds) and N is the number of Kuhn length. xs is defined as the volume ratio of the solvent molecule to the repeat units. The volume of CHCl3 (VC) is calculated to be 70.30 Å 3 ; the volume of tetrahydrofuran (VT) is computed to be 79.55 Å 3 ; the volume of the repeat units of PDHG-F is evaluated to be 1261.86 Å 3 . As a result, we accomplished xs = 0.056 for CHCl3 solvent and 0.063 for the tetrahydrofuran solvent respectively. β is defined as the expansion factor in which β > 1 corresponds to the expanded chains while 0 < β < 1 belongs to the collapsed chains. Commonly, β ranges from 0.33 to 0.7 if the chains are collapsed. 9,10 According to the equation ES1, β is determined by the Flory-Huggins interaction parameter χ where high χ indicates the poor compatibility between the solvent and the polymer chains while low χ suggests such good compatibility. In this case, high χ leads to dominantly intramolecular interactions between polymeric segments, which induces the chain collapses. On the contrary, low χ gives rise to dominant interactions between the solvent molecules and the repeat units, which enhances the excluded volume effect and supports the chain expansion or stretching. The χ can be calculated from the equation ES2 11 : χ = V(δP -δS) 2 / kT, where V is the monomeric molar volume (1261.86 Å 3 for PDHG-F); k is the Boltzmann constant; T is the temperature (298 K). As a result, χ is influenced by the term (δP -δS) 2 in which δP and δS are the solubility parameters of the polymer chains and the solvent molecules respectively. During the molecular dynamic calculation, the solubility parameters are divided into two-dimensional parameters in terms of van de Waals force (δP-vdW and δS-vdW) and electrostatic force (δP-E and δS-E) according to the calculation method of the COMPASS forcefield. 5 In this case, (δP -δS) 2 should be transformed to (δP-vdW -δS-vdW) 2 + 0.25 (δP-E -δS-E) 2 accodring to the reference 12 . According to the equation δ = (CED) 1/2 where CED is the cohesive energy density (involving δvdW = (CEDvdW) 1/2 , δE = (CEDE) 1/2 , referring to the literature 13 , we calculated the CED values of the PDHG-F chains, the CHCl3 solvent and the tetrahydrofuran solvent (As is shown in Supplementary Table 1).
In the light of Supplementary Table 1, the term (δP -δS) 2 of the PDHG-F and CHCl3 pair (3.49) is relatively lower than the PDHG-F and tetrahydrofuran pair (4.48). According to the equations ES1, the term (1/xs -2χ) is 8.99 for CHCl3 solution and 4.35 for the tetrahydrofuran. Considering C > 0 and N > 0, β > 1 is absolutely satisfied in this case because of the term β 5 -β 3 = β 3 (β + 1)(β -1) > 0. Moreover, if we further consider C ≈ 1/9 and N ≈ 1 for the rigid rod-like conformation of PDHG-F (DP = 9), we will evaluate β ≈ 1.242 for CHCl3 solution and β ≈ 1.152 for tetrahydrofuran solution. Therefore, the PDHG-F chains are expanded both in CHCl3 (to more degree) or tetrahydrofuran solutions. In this case, the chemical shifts of major hydrogen atoms on the PDHG-F chains should be the same as (or much approximate to) the meso-DHG4 or rac-DHG4 (DHG4 as the repeat unit).

Supplementary Note 5. Molecular weight calibration and calculation
The fundamental principle of GPC calibration 14,15 is derived from Mark-Houwink equation (ES3): = ES3 In the equation ES3, the exponent α is represented as Mark-Houwink constant which is associated with molecular conformation and solvents. K is represented as the constant that is related to polymer species, solvent environment, and temperature. The single polymeric size is linked to hydrodynamic volume Vh, which is proportional to ηM according to Einstein equation 14 (ES4): The elution volume is defined 16   , P(M) represents the polymeric fraction for the specific DP): The elution time t that corresponds to each specific DP (7~12) was evaluated via the extrapolation of the PDHG-F calibration equation (shown in Supplementary  Table 3) Supplementary  In the range of (4.3~1.0, 9.6~6.6). The cross-peak (3.90, 7.10) serves as the standard assigning to the space correlation of two hydrogen atoms between methoxyl and a-protons (intramolecular cases, shown in a black bend arrow). The anti-parallel stacking hypothesis is confirmed by the space correlation [cross-peak (1.30, 7.00)] between the methyl group (on the Cz moiety) and the a-proton (on the methoxybenzenyl group), as well as another correlation [crosspeak (1.30, 9.30)] between the methyl group (on the Cz moiety) and the N6-protons (on the DAF groups). Both space correlations are depicted in blue bend arrows. The crosspeaks are enclosed in the red boxes.
Supplementary Figure 23. The plausible gridization mechanism of MC1 that involves the carbocationic delocalization step. a The reaction pathways. b The balland-stick models of the likely intermediate V, VI, VII and VIII. The methoxybenzene moieties are marked in blue to stand out the stacking mode in the plausible dimer packing process. The tricationic species II easily undergoes the migration of the carbocation (III) 18 to obtain the quinonemethide-type intermediates IV 19 that performs structural planarization between the diazafluorene group and the benzoid moiety (fixed by double bonds). In this case, the cationic methoxybenzyl group probably interacts with the electron-donating carbazole moiety (via pi-pi stacking) and powerfully strengthens the centrosymmetric molecular packing V, which is favorable to meso-V VII VI VIII quinonemethide-type benzene-type b a selectivity. By contrast, the rotation of methoxybenzyl groups (VI) is unfavorable to the π-π stacking between two MC1 backbones. For the asymmetrically packing mode (VIII) that generates rac-DHGs, the quinonemethide-type intermediates IV likely make negligible contributions to enhancing molecular packing (VII), which is unable to efficiently improve rac-selectivity. Hence, the quinonemethide-type structures are seemingly favorable to centrosymmetric packing that enhances the meso-selectivity, which is confirmed by the rac-selectivity of tolyl-based MC2 substrates without quinonemethide-type species. Under these gridization conditions, the molar ratio of the water (released from MC substrates): CF3COOH: CF3SO3H is about 1:300:75. The 0.3% amount of water should not obviously lower the acidity of the media that is maintained by highly excessive equivalents of strong acids. According to Supplementary Figure 25 and Supplementary Figure 26, we tentatively found out the primarily kinetic laws of the polygridization controlled by supramolecular packing. As the polygridization performed in the bimolecular process, we use the second-order reaction rate expression ES14:dc/dt = kc 2 , where the c is defined as the concentration of the DC-F monomer; k is the reaction rate constant; and t is the reaction time. If the reaction rate constant is unchangeable during the polygridization process, we will obtain the equation ES15: DPn = c0kt + constant, where c0 is the initial concentration of DC-F monomers 20 . In this case, c0 is proportional to DPn. However, increasing c0 from 15 to 60 mM leads to decreasing the DPn from 9.2 to 8.0, which is contradictory to ES15. These results indicate that k should be decreased along with increasing c0. It is noted that increasing the monomer concentration enables to increase the supramolecular load of acid, which reduces the self-assembly efficiency 21 . As a result, k should be related to the supramolecular efficiency that is reciprocal to the monomer concentration: k ~ 1/c0 a , where the exponent a is slightly higher than 1. To further confirm this point, we observed the dependence of reaction times on DPn. We found that DPn is increased sharply in the beginning stage (0~6 s, the average polymerization rate of 1.4 DP s -1 ) while the following stage (6~25 s after the initiation) evidently lowered the polymerization rate to about 0.04 DP s -1 on average. Commonly, increasing the reaction time should enhance the DPn proportionally, like the typical cases 22 . As a consequence, we deduced that the reaction rate constant is high in the beginning stage but becomes much lower in the following polygridization stage, which is linked to the supramolecular packing of DC-F monomers in the beginning stage of the polygridization. Therefore, the reaction rate constant should be controlled by the supramolecular assembly efficiency.  Figure 29). During the collapsed process of meso-PDHG-F chains, it is initiated by chain folding based on the anti-to-syn conformational transitions of DHG-edges. Then, the contact of intramolecular segments driven by van de Waals force occurs toward the formation of the cluster. Deeply, increasing the chain length (by increasing the DP) enables to increase the number of the folding point (1~2 for DP = 7 and 9; 2 for DP = 13 and 6 for DP = 18) and thus decreased the average eccentricity of their ellipsoid models (in full collapsed equilibrium state) from 0.95 (DP = 7), 0.94 (DP = 9), 0.91 (DP = 13) to 0.85 (DP = 18). As a result, increasing the entropic driving force (via increasing the chain length) leads to decreasing the structural anisotropy of the collapsed backbones, which is consistent with the collapse of the traditional polymers 10 . However, all collapsed conformations belong to rod-like shape with higher anisotropy than that of rac-PDHG-F, independent of the chain length. For rac-PDHG-F, the similar cyclic skeletons derived from the conformational rotation between rac-DHG units and fluorene groups are all observed in DP = 7, 9 and 18, which are confirmed by the drastically fluctuating eccentricity of the ellipsoid models (e = 0.4~0.8). More interestingly, the full colllpased state of rac-PDHG-F is dependent on the DP where the short chains (DP = 7 and 9) transform into compact coil-like conformations (Supplementary Figure 27 and Supplementary Figure 28) but the long chains (DP = 13 and 18) lead to toroid conformations. These results suggest that the formation of toroid collapsed conformation requires enough entropic driving force. Moreover, whatever the coil-like or toroid backbones, rac-PDHG-F displays higher structural isotropy than meso-PDHG-F. In addition, when DP = 7, the collapsed rac-DHG-F chains have lower covalent energy, 9.4 kcal mol -1 per repreating units lower than that of meso-PDHG-F. For other chain length, rac-PDHG-F exhibits lower covalent energy as well, with corresponding differences (per repeat unit) involving 3.1 kcal mol -1 (DP = 9), 7.3 kcal mol -1 (DP = 13) and 10.8 kcal mol -1 (DP = 18). These results suggest that meso-PDHG-F increased the ability to prevent the chain collapse, which indicates higher rigidity. In all, even with entropic effects, the collapsed meso-PDHG-F still display the rod-like conformation with higher structural anisotropy and more unstably collapsed conformations than those of rac-PDHG-F. It is noted that the solubility of 3a is extremely poor (even using CF3COOH) and they are slightly soluble in DMSO. Even so, the white insoluble powder are precipitated during the 1 H NMR characterization which could interfere the results. The hydrogen signals of methylene on the carbazole can be only assigned to be at 4.29 ppm but with drastically large integration. Such signal is a singlet peak. Thus, the methylene signal can be overlapped with this peak. However, we can assign other peaks that testify this structure. For example, the 8.85 ppm peak with 5.2 Hz of coupling constant is assigned to N3/N6 positions of DAF groups. The 8.46~8.44 ppm peak (J = 8.0 Hz) is assigned to N1/N8sites on the DAF groups. The single signal at 7.88 ppm is merely assigned to be d-sites on the carbazole group because no other hydrogen atoms belong to the single signal. The dd peak of the signal at the 7.78 ~ 7.75 ppm is assigned to N2/N7-sites on the DAF groups because their two coupling constant 5.2 Hz and 8.0 Hz are corresponding to the coupling of N3-N2 (or N6-N7) and N2-N1 (or N7-N8). The doublet peak at 7.62 ~ 7.59 ppm is assigned to f or g-sites at the carbazole group. The teiplet signal at the 1.23 ~ 1.20 ppm is assigned to the methyl group on the carbazole segment. What's more, the integration ratio of N3/N6 to i (meanwhile, N3/N6 to f or g) is equal to 2. Similarly, the integration ratio of N3/N6 to methyl group is equal to 4:3 instead of 2:3. Therefore, the 3a structure is the disubstitution of DAF on the ethyl-carbazole in the Friedel-Crafts reaction.

Supplementary
Supplementary Figure 42. 13 C NMR spectra for 3a in d6 -DMSO. Analogously, due to extremely poor solubility, the 13 C NMR spectra is not good. However, based on the deduction of the 1H NMR spectra, we considered that the signal ranging from 40.3 to 39.2 ppm should be assigned to the methylene group (at the carbazole segment) that is overlapped by the solvent DMSO (39.52 ppm). Considering such carbon signal is at 37.6 ppm for 2a (in CDCl3 solvent), this signal is indeed likely to be distributed at the 40.3 ~ 39.2 ppm. a It is noted that the solvents of DCM and methoxyl-alcohol were participated in the single crystallography. The A-typed errors were only focused on the solvent molecule.

Supplementary
There is no A-typed errors for rac-DHG1 backbones.