Synthesis and Characterization

We previously established the two-step synthesis of fjord-methoxy substituted [n]HDIs (n = 5–7) employing a building-block based strategy: 1) The coupling of homophthalimide derivative 2 with aromatic dialdehydes in a Knoevenagel reaction to form stilbene-like precursors, followed by 2) Mallory photocyclodehydrogenation (PCD) to yield [n]HDIs (n = 5–7).^{[34, 65]} This approach was used as the starting point for the synthesis of the [8]HDIs (Route 1, Scheme 1). The first challenge was obtaining the [4]helicene dialdehyde 1. While this compound is known, the only reference mentioning it did not provide synthetic details.^[68] We therefore developed a synthetic strategy starting from 2,7-dibromonaphthalene to yield 1 over four steps in 56% overall yield (Section S2). However, we encountered problems in the PCD step upon attempting to prepare N-nBu-[8]HDI-f-OMe. While the precursor 3 was obtained in 44% yield, in the PCD reaction even after several days only 8% yield could be achieved.

We therefore developed an alternative synthetic pathway (Route 2, Scheme 1) with the main difference being the use of homophthalic acid dimethyl ester (4) in the Knoevenagel reaction in place of 2, with consequent conversion of the [8]helicene tetracarboxylic ester 6 resulting from the PCD reaction into the [8]helicene dianhydride 7 with an excess of p-toluenesulfonic acid monohydrate, and subsequently reacting 7 with the appropriate amine to obtain the target [8]HDIs. Crucially, the PCD reaction from 5 to 6 is possible in significantly larger quantity (on the order of a few hundred milligrams), shorter reaction time (24 h) and with much higher yields (−50%) compared with the earlier procedure, likely due to the electron-rich nature of 6 compared with 3.^{[57, 69]} Even though this pathway requires more steps than route 1, it is more versatile: The enantiomeric separation via HPLC employing a chiral stationary phase (CSP) column can take place with 6 and does not have to be optimized for each new final compound. Additionally, the dianhydride 7 can serve as a starting point for a variety of target molecules, like the extensive chemistry that has been developed for rylene diimides starting from their respective anhydrides.^[70-72]

While the open dialkyl-[8]HDIs, (N-nBu-[8]HDI and N-Me-[8]HDI), which serve as reference compounds, could be obtained in good yields by straightforward reaction with an excess of amine in propionic acid, synthesizing the alkyl-bridged [8]HDIs (C_m-[8]HDI, m = 3–6) required careful tuning of the reaction conditions. Although the ring closure is kinetically favored, the numerous possible side reactions, including oligomer formation or reaction with two equivalents of diamine, made optimizing the reaction conditions challenging. Through the high dilution principle of Ziegler and Ruggli,^[73] achieved by slow addition of one equivalent of the respective diamine, and a concentration of the anhydride of − 2 × 10⁻⁴ M in toluene with imidazole and pyridine as co-solvents, it was however possible to obtain C_m-[8]HDI (m = 3–6), with yields between 41% and 57%. 6 was resolved into its enantiomers by HPLC on a semi-preparative CSP column (Figure S19 and Table S6). The reactions with enantiomerically pure 6 gave similar yields for imidization as with rac-6. The enantiopurity of the products was ensured by analytical CSP–HPLC. Owing to the high kinetic stability of [8]helicenes,^{[6, 74]} no racemization took place during the reaction. The structures of the obtained compounds were unambiguously confirmed by 1D and 2D ¹H and ¹³C NMR measurements (Section S8), high-resolution mass spectrometry (Section S9), and single-crystal X-ray analysis (Section S7).

Effect of the Helical Pitch on the Solid-State Structures and Molecular Packing

The effect of the different alkyl bridges on the helical pitch, and consequently the molecular packing, was investigated by X-ray crystallography. Single crystals were grown by various diffusion and evaporation methods for all racemic [8]HDIs, as well as enantiopure C₃-[8]HDI and C₄-[8]HDI and N-Me-[8]HDI (Section S7). The expected structures were confirmed, and the strong influence of the length of the alkyl bridge on their helical backbone was revealed.

The key parameters defining the geometry of a classical spring—its helical pitch P and coil angle α—have direct equivalents that can be measured in the respective crystal structures (Figure 2). The helical pitch can be approximated by the distance between the carbon atoms at the intersection between the [8]helicene and the imide ring (d_C–C), and 2α by the torsion angle between the 3^rd and 6^th carbon-carbon bonds within the inner helix of the backbone. d_C–C increases from 3.304 Å in C₃-[8]HDI to 3.878 Å in C₆-[8]HDI, and 2α increases from 35.3° to 38.8°. Notably, the 2α value of 33.9° for N-Me-[8]HDI is lower than that of all bridged [8]HDIs, which is likely due to strong intermolecular dipole–dipole interactions between the imide groups facilitated by the crystal packing—the DFT-optimized structure shows the expected intermediate value with 38.2° (Table S17). Hence, as we hypothesised, the helical pitch of [8]HDI can be restrained in different compressed or extended states by variation of the bridge length. The experimental values for d_C–C correlate well with the ones obtained from DFT calculations. A third characteristic, exclusive to the [8]HDIs, is the dihedral angle between the planes defined by the imide rings, as a measure of the distortion of the structure by the bridging alkyl chain (Figure S32). While the planes of the imide rings are pushed apart with a significant angle of 26.2° in C₆-[8]HDI, in C₃-[8]HDI they are squeezed together, pointing towards each other with an angle of −4.1°. These changes in overall geometry have a considerable effect on the crystal packing patterns (Figure S34).

The crystal packing of rac-C₃- and rac-C₄-[8]HDI consists of alternating homochiral columnar stacks, with partially interlocking backbones of (P) and (M) enantiomers in their respective columns, held together mainly by π–π-interactions. A comparable arrangement can be found in two polymorphs of rac-N-Me-[8]HDI. In rac-C₅-[8]HDI crystals, this arrangement changes to stacks of alternating (P) and (M) enantiomers. rac-C₆-[8]HDI forms homochiral columns similar to rac-C₃- and rac-C₄-[8]HDI, however here the individual molecules in the stacks are offset by 180° with respect to each other. The longer-chained rac-N-nBu-[8]HDI shows a complicated arrangement due to the larger volume taken up by the alkyl chains. The enantiomerically pure compounds exhibit different crystal packing compared with the racemic compounds. For (M)-C₃-[8]HDI, the crystal consists of homochiral stacks in which each stacked molecule is turned by 90° in the opposite direction as the helical backbone, while for (M)-C₄-[8]HDI, the individual molecules within the columnar structures are all oriented parallelly, but each column is turned by 90° with respect to its neighbors. (P)-N-Me-[8]HDI exhibits a herringbone-like packing consisting of sheets of aligned molecules, but in contrast to a true herringbone pattern there are not two, but four distinct orientations which repeat in the crystal.

Effect of the Helical Pitch on the Optical Properties

The target compounds were all obtained as crystalline, bright yellow solids exhibiting greenish fluorescence in solution. Their absorption spectra are only weakly influenced by the helical pitch—except for a shift of the weak first absorption peak towards longer wavelengths with lower pitch (Figure 3a). The first absorption maximum, around 460 to 475 nm, is of small magnitude, with extinction coefficients of between 1200 m⁻¹ cm⁻¹ for C₃- and C₄-[8]HDI to 1600 m⁻¹ cm⁻¹ for C₅- and C₆-[8]HDI (in toluene), with the non-bridged analogs taking up intermediate values (Tables 1 and S1).

In contrast, the helical pitch of the backbone has a large influence on the emission spectra. While all compounds show a similar emission profile (Figure 3b), there is a notable bathochromic shift with decreasing helical pitch. This can be explained by selective stabilization of the LUMO by through-space interactions between the imide groups, and consequently a smaller optical energy gap (Tables 1 and S5). The non-bridged reference compounds (N-Me-[8]HDI and N-nBu-[8]HDI) show similar absorption and emission profiles with emission maxima at 480 and 479 nm, respectively, indicating a negligible effect of the length of the alkyl chains on the optical spectra. Therefore, the bathochromic shift of C₃- and C₄-[8]HDI and the hypsochromic shift of C₅- and C₆-[8]HDI with respect to these reference compounds can be solely attributed to the compression or extension of the molecular spring imposed by the alkyl bridges. The similar vibronic structures of the emission spectra of all compounds indicate that, despite the large structural changes, the rigidity of the fluorophore is only weakly dependent on the helical pitch.

While there are no pronounced solvent effects in the absorption spectra, a distinct bathochromic shift of the fluorescence can be observed with increasing solvent polarity in all compounds in the series toluene, chloroform, THF, and DMSO (Section S3.2). In toluene, there is a clear vibronic progression in the emission spectra, while in polar DMSO, the features of the spectra are mostly obscured by line broadening.

The photoluminescence quantum yields of all compounds are around 0.05, and the fluorescence lifetimes range between 5 and 7 ns. Therefore, the rate constants for both the radiative and non-radiative processes are similar in all compounds (Tables 1 and S1–S4). In contrast to earlier studies on the effects of strain on spring-like helicenes,^{[52, 76, 77]} in the [8]HDIs, the changes in the helical pitch of the molecular backbone do not lead to significant fluorescence quenching or acceleration of non-radiative decay modes.

TD–DFT calculations (B3LYP/6–311G(2d,p)//ωB97XD/6–31g(d,p)) provide further insights into the electronic transitions responsible for the absorption spectra. For the C₃-, C₄-, and C₅-bridged [8]HDIs, the lowest-energy electronic transition consists mostly of the HOMO → LUMO transition with relatively low oscillator strengths of 0.015 to 0.018, in line with the low extinction coefficients of their observed absorption peaks (Table S9). In contrast, the same transition for C₆-[8]HDI, as well as for the non-bridged [8]HDIs, shows a significant contribution from the HOMO–1 → LUMO transition, with similar oscillator strengths (except for C₆-[8]HDI which shows f = 0.029). In this context it is notable that the HOMO and the HOMO + 1 are almost degenerate in all compounds, while the energetic difference between the LUMO and the LUMO + 1 decreases with the length of the bridging alkyl chain.

Effect of the Helical Pitch on the Chiroptical Properties

The enantiomerically pure [8]HDIs exhibit a pronounced chiroptical response (Figure 4). Their absolute configurations were assigned by comparing the experimental and calculated CD spectra. Additionally, the absolute configurations of (M)-C₃-[8]HDI, (M)-C₄-[8]HDI, and (P)-N-Me-[8]HDI could be confirmed by the Flack parameter in their crystal structures. The experimental and the calculated spectra are in good agreement (Figures S21–S22). The CD spectra show three major peaks in the visible and near ultraviolet regions of the spectral range. The second peak (380–450 nm) reaches substantial Δε values ranging from 90 m⁻¹ cm⁻¹ for C₃-[8]HDI to 170 m⁻¹ cm⁻¹ for C₆-[8]HDI, while the first peak (450–500 nm) coincides with the lowest-energy absorption peak and exhibits a somewhat smaller Δε. With decreasing helical pitch, the rotary strength of the first peak increases, while that of the second and third peaks decreases. Concomitantly, the low-energy transitions in the absorption spectra exhibit much lower extinction coefficients, indicating a relatively high g_abs factor. Indeed, all [8]HDIs show their maximum g_abs value in the vicinity of the first peak in the CD spectrum. These values range from 3.1 × 10⁻² for non-bridged N-Me- and N-nBu-[8]HDI—similar to pristine [8]helicene^{[78, 79]}—up to 5.6 × 10⁻² in C₃-[8]HDI and are similar across solvents of varying polarity (Tables S1–S4). The correlation between helical pitch and g_abs shows a perfectly linear relationship for the bridged compounds, while the open-chained [8]HDIs form outliers on the low side (Figure 4c). Remarkably, the curve shapes and g_abs values for wavelengths below 450 nm are similar in all tested solvents for all compounds, indicating that the lowest-energy transition is the only one affected by the geometry changes (Figures S11 and S13–S15).

The CPL spectra of the [8]HDIs show similar features as their fluorescence profiles, albeit with a less pronounced vibronic structure, as the lower-energy bands show a proportionally smaller CPL signal compared with the fluorescence spectra (Figure 4b). Accordingly, the g_lum plots reach their respective maximums around the emission peak for all compounds. The g_lum values range from 3.1 × 10⁻² for C₆-[8]HDI to 6.0 × 10⁻² for C₃-[8]HDI, like the g_abs values exhibiting a linear relationship with helical pitch. A similar linear relationship between helical pitch and dissymmetry factors has previously been observed in helical BODIPY dimers,^[53] however in that case better performance was correlated with an increase in helical pitch, while in the C_m-[8]HDIs, it is instead associated with a decrease in pitch. Again, the open-chained N-Me-[8]HDI is in an outlier position with a significantly lower value (Figure 4c). The g_lum plots show a clear peak structure (Figures S11 and S13–S15), which is unusual, as most compounds exhibit a nearly constant g_lum over the whole width of the emission spectrum.^[80] Together with the g_abs of similar magnitude, those are among the largest values recorded for helicene-type molecules,^{[8, 10, 11, 81-89]} only exceeded among purely organic compounds by some chiral carbon nanotube wall segments^[90] and similar molecules featuring cylinder chirality,^{[91, 92]} as well as some self-assembled macrocycles.^[93] The similar values of g_abs and g_lum indicate no excimer formation despite the large overlap of the termini of the helicene backbone and the imide groups.^[94] While helicene-derived molecules often show significantly lower g_lum compared to the g_abs values,^{[10, 80]} the discussed compounds exhibit similar values, implying minute structural reorganization in the excited state.

To elucidate the influence of the helical pitch on the chiroptical properties, supporting TD–DFT calculations were performed to obtain the values for the electric (µ_e) and magnetic (µ_m) transition dipole moments for the S₀ → S₁ and S₁ → S₀  transitions (SI Tables S8.1 and S8.2), since the g values arise from the interplay of these factors as derived in the following equation:^[95] $$, with θ being the angle between the vectors of the two dipole moments. The value for g is maximized for µ_e and µ_m that are equal in magnitude and either parallel or antiparallel. Therefore, while the low µ_e of the S₀ → S₁ transition (vide supra) impedes its absorptivity, it has the advantageous effect of leading to a relatively high chiroptical response, as the low value for µ_e makes it closer in value to µ_m, which is usually much lower for small organic molecules. In agreement with the experimental g values, going from larger to smaller helical pitch, µ_e (in 10⁻²⁰ esu cm) decreases from 166 for C₆-[8]HDI to 123 for C₃-[8]HDI, while µ_m (in 10⁻²⁰ erg G⁻¹) increases from 1.90 to 2.18. Crucially, this means that the high g values observed for the shorter-bridged compounds are not merely a result of the small µ_e in their lowest-energy transitions, but can concomitantly be attributed to an increase in their µ_m. Compared with their bridged analogs, the open-chained compounds N-Me-[8]HDI and N-nBu-[8]HDI show similar µ_e to C₃-[8]HDI, but their µ_m are notably lower. From the calculated values for µ_e and µ_m, as well as the angle θ between them, g_abs values were obtained and compared to the observed experimental values (Tables S8.1 and S8.2).^[96] The calculated values are in good agreement with the experimental ones, albeit slightly overestimating them, in particular for the longer-chained compounds. Plotting µ_e, µ_m, and cos θ for the S₀ → S₁ transition against the helical pitch provides an overview of how these values are affected by the helical pitch (Figure 4d). The observed increase in g values with decreasing helical pitch therefore results from a concurrent decrease in µ_e and an increase in µ_m, while cos θ remains nearly constant. A direct relationship between the rotational strength R of electronic transitions in helical molecules and the radius r and pitch P was first shown by Tinoco and Woody in 1964 using the simple free electron on a helix model.^[97] A recent theoretical study further demonstrated a linear relationship between µ_m and the area enclosed by the backbone of helicene-like molecules.^[98] A similar mechanism might be responsible for the increase in µ_m and dissymmetric factors in the shorter-bridged [8]HDIs.

Effect of the Helical Pitch on the Electrochemical Properties

In our previous work, we demonstrated how the interplay of through-space and through-bond interactions between the imide groups on the smaller [n]HDIs (n = 5–7) influences their redox behavior.^[34] We established that bringing the imide groups—and thus, the redox centers—closer together in space can compensate the decreasing conjugation through the twisted backbone of the molecules with increasing length of the helicenes. The maximum through-space conjugation was observed in [7]HDI, where two terminal benzene rings of the [7]helicene backbone are overlapping. For the [8]HDIs, we anticipated an enhanced through-space conjugation due to the position of the terminal naphthalimide moieties directly on top of each other (Figure 1a). The electrochemical properties of the bridged [8]HDIs and the reference compounds N-Me-[8]HDI and N-nBu-[8]HDI, as well as fjord-methoxy substituted N-nBu-[8]HDI-f-OMe (Figures 5, S16–S18 and Table S5) were probed by cyclic voltammetry (CV) and differential pulse voltammetry (DPV) measurements. As expected, all [8]HDIs show two distinct, reversible reduction waves in the CV and two symmetrical peaks in the DPV plots, corresponding to sequential one-electron reduction of the two imide units. In contrast, no oxidation could be probed within the electrochemical window of THF.

Several trends became apparent: 1) The value of ΔE_red for N-nBu-[8]HDI-f-OMe (0.25 V) is indeed the largest among the homologous series of fjord-methoxy substituted [n]HDIs (n = 5–8), confirming that the through-space conjugation of the imide groups reaches a maximum for this compound. The other two non-bridged [8]HDIs show slightly lower values of ΔE_red (−0.23 V)—for both N-Me-[8]HDI and N-nBu-[8]HDI—due to the absent methoxy group. 2) All bridged compounds exhibit a larger value for ΔE_red compared with the non-bridged reference compounds. 3) ΔE_red increases with decreased helical pitch from 0.26 V for C₆-[8]HDI to 0.30 V for C₃-[8]HDI, although the value for C₄-[8]HDI is similar to that for C₅-[8]HDI despite the increase in helical pitch in the latter. This indicates that other effects, such as electronic communication through the alkyl bridge, may play a role as well.

The redox potential of the first reduction steadily decreases with the helical pitch, corresponding to easier reduction and consequently a lower LUMO level, while the HOMO level stays nearly constant for all investigated compounds (Figure 5 and Table S5). This can be rationalized by the greater stabilization of negative charges by two spatially close imides, which is further supported by the calculated molecular electrostatic potential surfaces (MEPs) of the radical anions (Figures 5b,c and S23), where it becomes apparent that the negative charge is more delocalized between the two imide units in the molecules bearing a shorter bridging chain. Likewise, the calculated LUMO of the neutral molecule shows significantly increased through-space orbital overlap in C₃-[8]HDI compared with the higher homologs (Figures 1b and S20).

The strong electronic coupling between the two redox centers is further supported by the (TD)–DFT calculated intervalence charge transfer (IV–CT) parameters (Table S10) of their radical anions. The calculated electronic coupling (V₁₂) values can serve as a quantitative measure of electronic communication between the two redox centers.^{[99, 100]} As anticipated the calculated values for V₁₂ show an inverse relationship with the helical pitch (Figure 5d)—the V₁₂ value for C₃-[8]HDI (1902 cm⁻¹) is nearly double that for C₆-[8]HDI (922 cm⁻¹), which demonstrates that the electronic coupling between the redox centers is strongly dependent on their through-space distance, further supporting the CV and DPV data (Table S10).^[101-103] Similar to their smaller homologues ([n]HDI, n = 5–7), the V₁₂ values for the radical anions of all [8]HDIs are smaller than half of their reorganization energy (V₁₂ < λ / 2), which classifies them as Robin−Day class II mixed-valence compounds.^[104]