A minimal cage of a diamond twin with chirality.

A network of tetrahedral vertices can fill three-dimensional (3D) spaces in a beautiful and isotropic manner, which is found as diamonds with sp3-hybridized carbon atoms. Although a network of trigonal vertices (i.e., another form of carbon atoms with sp2-hybridization) naturally results in a lower-dimensional two-dimensional network of graphenes, an isotropic 3D arrangement of trigonal vertices has been of theoretical and mathematical interest, which has materialized as a proposal of a "diamond twin." We herein report the synthesis and optical resolution of a minimal cage of a chiral diamond-twin network. With triangular phenine units at 14 vertices, triply fused decagonal rings were assembled by forming 15 biaryl edges via coupling. A unique chirality of the network has been disclosed with the minimal cage, which may stimulate explorations of chiral carbonaceous materials.

The hybridization of carbon atoms plays an important role in determining the structures of their networks because the intrinsic geometries of sp3-, sp2-, and sp-carbon atoms dramatically alter the shapes of their tetrahedral (three-dimensional [3D]), trigonal (two-dimensional), and linear (one-dimensional) forms. A four-hand, tetravalent hybridization of sp3-carbon is fascinating to not only lay people but also scientists through the beauty of diamonds, which has led chemists to explore segmental cages of diamondoids with adamantane as the minimal carbonaceous cage (1, 2). Recently, the beauty of 3D networks of sp3-carbon atoms in diamonds has also been captured by mathematics adopting algebraic topology (3). Thus, the diamond crystal has been defined as a maximal abelian covering graph (MACG) of a quotient graph 1 (Fig. 1), which clarifies the presence of the strongly isotropic network of vertices (A, B) and edges (a–d) (4). This mathematical approach [i.e., topological crystallography (5)] has led to the rediscovery of a hypothetical diamond twin that is hereafter described as pollux in this work, after the younger brother in the Gemini twins. Indeed, the pollux has long attracted theoretical interest (6–8) and is mathematically redefined as a diamond twin due to its strong isotropy with maximal symmetry (3) (). Thus, pollux is an MACG of quotient graph 2 and shares topological beauty with diamond by achieving the maximal symmetry in filling 3D spaces (Fig. 1). In place of the four-hand vertices of diamond, pollux adopts three-hand, trivalent vertices of sp2-carbon atoms; by linking four types of vertices (A–D) with six types of edges (a–f), the 3D spaces are filled in a strongly isotropic manner. Notably, unlike other isotropic carbonaceous networks of diamond or graphene, the isotropic pollux network gives rise to chirality, and two enantiomeric forms have been predicted. However, although this mathematical proposal is intriguing, the existence of pollux has been naturally questioned due to the highly strained, twisted orientations of connected sp2-carbon atoms (6, 9, 10). Actually, when we examined a minimal cage segment of pollux, herein named polluxene, by density functional theory (DFT) calculations at the B3LYP/6-31G(d,p) level, it was not located as a stable molecule and collapsed into ring-closed [4.4.4]propellahexaene (Fig. 1) (11). Nonetheless, we realized that by preassembling six sp2-carbon atoms in the form of 1,3,5-trisubstituted benzene (phenine) (12), a homothetic polluxene cage composed of sp2-carbon atoms could be rationally designed. By using phenine as the trivalent, trigonal planar units, the minimal carbonaceous cage of pollux was thus realized in the form of phenine polluxene to cover all fundamental vertices and edges of quotient graph 2 in 3D space with a fused decagonal cage (Fig. 1). The synthesis of phenine polluxene allowed us to deliberate the structures and chirality of the pollux network, which clarified the presence of unique helical chirality. The chirality and stereoisomerism of pollux thus give us intriguing targets to exploit for the development of chiral carbonaceous materials (13).

Fig. 1.

Strongly isotropic networks revealed by topological crystallography. Diamonds and polluxes were found to be strongly isotropic MACGs that were derived from corresponding quotient graphs with tetravalent and trivalent vertices, respectively. Adopting fundamental vertices and edges, MACGs gave rise to minimal cages of adamantane and polluxene as segmental molecules. Polluxene composed of sp2-carbon atoms was not located as a stable molecule by DFT calculations at the B3LYP/6-31G(d,p) level and collapsed into a ring-closed [4.4.4]propellahexaene molecule. Replacing sp2-carbon atoms of polluxene with phenine resulted in the phenine polluxene that was conceived and synthesized in this work.

Results and Discussion

Synthesis.

The trivalent vertices of phenine units need to be linked to form triply fused decagonal macrocycles to form the minimal carbonaceous cage of pollux (3). For the synthesis of this unique decagonal cage, a stepwise ring-closing route was developed after unsuccessful trials of bisectional routes (Fig. 2) (14, 15). A linear precursor (5a) for the first decagonal macrocycle was thus synthesized by a method developed for materials applications (16), and after conversion to 6a via borylation (17), dimerization via Ni-mediated Yamamoto coupling was performed to synthesize the decagonal macrocycle (7a) having eight t-Bu and two boryl substituents. The macrocycle was furnished with two biphenyl units (8a), which were closed for a transannular bridge via 9a to afford phenine polluxene 10a comprising 14 trivalent vertices linked with 15 biaryl edges. The feasibility of the final ring-closing reaction was indeed expected by two relevant facts. First, we expected that the decagonal macrocycle should adopt a conformation similar to methano[10]annulene (18, 19), which should set the biphenyl rims at preferable positions to close the transannular, bascule bridge. Second, the biaryl linkages used as the edge of the minimal cage can tolerate bond rotations and, unlike highly conjugated bonds between sp2-carbon vertices, can adopt the twisted orientations required by the mathematical demand to fulfill the polluxene network (5). The synthetic route was versatile enough to tolerate different substituents to expand the phenine network, and phenine-expanded polluxene 10b was likewise synthesized. The effects of phenine expansion were preliminarily examined by absorption spectra. Thus, the absorption onset of 10a with an 84π-system appeared at 313 nm, which was redshifted to 326 nm with 10b having a larger 156π-system (Fig. 2).

Fig. 2.

Synthesis of phenine polluxene congeners. (A) Five-step synthesis of phenine polluxenes 10a and 10b with different substituents on the minimal cage. (B) Ultraviolet-visible (UV-vis) absorption spectra of 10a and 10b in chloroform at 25 °C.

Crystal Structure and Chirality.

The synthesis of the minimal cage in the form of phenine polluxene allowed us to clarify the uniqueness of the chirality of the fused decagonal cage via a series of structural analyses. We first clarified the molecular structure of 10a by single-crystal X-ray crystallography. Although there were potentially many possible isomeric structures (see Stereoisomerism), phenine polluxene existed as a pair of enantiomers in the crystal. The enantiomer pair of 10a emerged from the chirality due to the D3 point symmetry, which was detailed by scrutinizing the molecular structure (Fig. 3). Thus, a pair of bridgehead phenine panels were triply connected by looped phenine bridges to form a nanometer-sized cage. Depicting phenine panels of the crystal structure with round disks allowed us to clarify the presence of symmetry operations, and one C3 axis and three C2 axes were found to render the overall structure of the D3 point symmetry. When the molecule was viewed along the C3 axis that penetrated phenine vertices, the helicity associated with D3-10a became evident. For instance, with the enantiomer shown in Fig. 3, all three bridges formed right-handed screws around the C3 axis (Fig. 3), and its mirror-image isomer possessed screwed bridges in an opposite sense (see Fig. 3). Thus, two enantiomers can be discriminated as a mirror-image pair by considering the helical sense of the screwed bridges around the C3 axis; by taking into account the helicity nomenclatures of IUPAC (20), we propose to designate the stereoisomer with right-handed screwed bridges as the (P)-isomer. With this designation, the crystal packing containing (P)- and (M)-enantiomers of 10a can be discriminated and designated in a clear manner, as shown in Fig. 3 (21). Notably, as the C3/C2 axes of polluxene were inherited from the infinite pollux network in the I4132 space group (see Fig. 1) (6, 7, 22), the helicity nomenclature for polluxene can be directly applied to pollux. Thus, we may define the nomenclature in general as follows. When viewed along the C3 symmetry axis penetrating a trivalent vertex, pollux/polluxene possesses three bridges that connect one vertex on a front side to another vertex on a back side. When the bridges are screwed to form right-handed helices, pollux/polluxene is designated (P), whereas those with left-handed helices are designated (M).

Fig. 3.

Molecular structures of phenine polluxene. (A) Crystal structures of 10a. In addition to the standard molecular models on the left, schematic representations with symmetry operations are shown on the right. Schematic representations were created by using the coordinates of the crystal structure and replacing phenine panels with disks. As a representative structure, one of the enantiomers is shown. (B) An enantiomer pair of 10a in the crystal packing. (C) Theoretical structures obtained from the conformational search analyses of 10a with methyl substituents. Two enantiomeric structures are shown in red/blue, and low-energy stereoisomeric structures are shown in gray. Within an energy window of 3 kcal ⋅ mol−1 from the global minimum, 12 isomeric structures were found. A Boltzmann-weighted average structure of the isomeric structure is shown in black.

Stereoisomerism.

The stereoisomerism of the fused decagonal cages was further investigated in detail with the aid of combinatorial enumerations based on group theory. In general, enumeration of stereoisomers is the most fundamental and important step to get a whole picture of the stereoisomerism, and due to complicated topologies of cyclic systems, the structural mathematics is indispensable (13, 23). The stereoisomerism of phenine polluxene is complicated due to its cyclic and fused structure comprising 14 vertices connected with 15 edges. The edges were composed of twisted biaryl bonds that intrinsically possessed chirality axes. As a result, 215 (= 32,768) redundant combinations of atropisomeric bonds emerge in total, which further gives rise to the unique cycloisomerism of a cage system (13, 24). To further elucidate the isomerism, we applied a combinatorial enumeration method that was derived from Pólya’s theorem (25, 26). Thus, 10a with D3 point symmetry possesses a nonredundant set of subgroup (SSG) of {C1, C2, C3, D3}, and by taking into account the isomeric structures, we obtain a vector, (215 28 25 23), as the SSG of phenine polluxene. Then, by applying the inverse of the table of marks for the D3 point group to the SSG, we derive the total numbers of isomers as follows:

Thus, the total number of the nonredundant isomeric structures of 10a reaches 5332 + 248 + 12+ 8 = 5,600.

Structural Fluctuations in Solution.

Theoretical calculations further deepened our understanding of the chiral polluxene structure in solution. Among the 5,600 nonredundant structures, only 12 isomers (six enantiomer pairs) were found within an energy range of +3 kcal ⋅ mol−1 from the global minimum via conformational search calculations (MM2* and CHCl3) with a model having methyl substituents () (27). The structure at the global minimum possessed D3 point symmetry and reproduced the crystal structure of (P)/(M)-10a (see Fig. 3). As expected from the ortho-substituent–free structure, the energy barrier for epimerization at the biaryl linkage was small. For instance, the energy barrier for the conversion of the global minimum structure to the second-stable structure was estimated as +3 kcal ⋅ mol−1 (), which suggested rapid interconversions of isomeric structures. Thus, the results suggested that when (P)- and (M)-10a racemate was dissolved in solution, rapid interconversions of conformers proceeded at ambient temperature, which resulted in the D3h point symmetry of the average structure (Fig. 3).

Chiral Polluxene.

Taking advantage of the concise synthetic route, we then synthesized rigid chiral polluxenes and succeeded in chiral resolution. Considering that biaryl atropisomerism plays a determinant role in determining the helical chirality of polluxene, we installed an ortho-dimethylated linkage at one of the bridges for stereochemical rigidity. In the first preliminary attempt, dimethylated derivative 10c was prepared (Fig. 4), but the chiral resolution was not successful after examination of five different types of chiral columns. Realizing that the chiral cage should be concealed by radiated substituents, we then introduced two extra methoxy groups as auxiliary groups to facilitate chiral recognition. Consequently, we were delighted to find that a chiral column loaded with (R)-1-naphthylglycine succeeded in separating the two stereoisomers of (+)300/(−)300-10d (Fig. 4) (28). Preliminary theoretical investigations on the rotational barrier indicated the presence of a high barrier of >30 kcal ⋅ mol−1. The separated isomers gave mirror-image circular dichroism (CD) spectra (Fig. 4), which confirmed the enantiomeric relationship between these two isomers. The conformational search calculations of 10d with methyl substituents located a pair of enantiomers as the global minimum (Fig. 4), which should exist as the most abundant structures in solution (∼50% population of Boltzmann distributions). The conformational analyses also suggested that both the dominant structure and the Boltzmann-weighted average structure possess single-sense helices around the pseudo C3 axis. Thus, (S)-biaryl linkages of 10d resulted in right/right/right screwed bridges both in the average and global minimum structures, and hence the structure should best be represented as (P)-10d (). We then performed time-dependent (TD) DFT calculations to simulate a theoretical CD spectrum from the global minimum structure of (P)-10d; as shown in Fig. 4, the spectrum matched well with that of (+)300-10d. Further confirmation of X-ray crystallography should be performed in the future to confirm the configurational assignment of the helicity. Nonetheless, a pair of enantiomers was separated with the rigid chiral polluxene derivative to afford two stereoisomers with mirror-image CD spectra.

Fig. 4.

Chiral resolution of polluxene. (A) Synthesized polluxene (10c and 10d) with stereochemical rigidity. (B) Chiral resolution of 10d. A chiral column loaded with (R)-1-naphthylglycine (SUMICHIRAL OA-2500, 4.6 × 250 mm) was used for the HPLC analyses (eluent = 0.5% 1-butanol/hexane; flow rate = 1.0 mL ⋅ min−1, 40 °C). Stereoisomers were labeled with the CD sign at 300 nm. (C) CD spectra of enantiomers of 10d in chloroform at 25 °C. A theoretical CD spectrum was obtained by TD DFT calculations at the B3LYP/6-31G(d,p)/PCM level with the (P)-isomer of 10d having a methyl substituent. (D) An enantiomer pair found as the global minimum from the conformational search calculations of 10d with methyl substituents (). The chromatographic chiral resolution of (+)300- and (−)300-enantiomers showed that these enantiomeric structures are not interconverted in solution at ambient temperature.

Conclusions

The trivalent planar units of phenine were assembled as vertices of fused decagonal cycles to form a minimal cage of the diamond twin, pollux, which added a unique example to modern repertoire of molecular cages (14, 15, 29–31). Although pollux has been an imaginary, long-sought entity of theoretical interest (3, 6), the synthesis of the minimal cage showed that it now becomes a reachable, synthetic target by adopting stable trivalent units such as phenine. The nanometer-sized cage, named phenine polluxene, revealed a unique molecular structure both by experiments and in theory to demonstrate the presence of a chiral network. The chirality of the pollux/polluxene networks originated from the helicity around the major C3 axis, which should be discriminated by the triple helix made of three screwed bridges around the C3 axis. Asymmetric syntheses and expansions of the phenine networks should be an intriguing target to be explored in the next stage for chiral carbon-rich materials.

Materials and Methods

Phenine polluxenes (10a-d) were synthesized by a common stepwise route combining multiple biaryl coupling reactions. Structures were identified by spectroscopic analyses with proofs of purity from high-performance liquid chromatography (HPLC) analyses. Chiral resolutions of 10d were chromatographically achieved by using SUMICHIRAL OA-2500 columns. Further details of procedures and results are described in .

Crystallographic Analysis.

A single crystal of phenine polluxene 10a suitable for X-ray analysis was obtained by slow diffusion of methanol into chloroform solution at 25 °C. The diffraction analyses were carried out at −180 °C on a Rigaku XtaLAB P200 diffractometer equipped with a PILATUS200K area detector using multilayer mirror monochromated Cu-Kα radiation. From the diffraction data were obtained the structure by using the SHELXT program (32) for initial phase determination and the SHELXL program (33) for structural refinements of full-matrix least squares on F2 on the Olex2 program (34). Further details of analyses are described in .

Theoretical Structural Analysis.

Conformational search analyses of phenine polluxenes 10a and 10d were performed with MacroModel (35) to reveal structural fluctuations in solution. For the detailed energetics and spectral simulations, DFT calculations were performed with Gaussian 16 (36). Further details of calculations are described in .