Can aromaticity be a kinetic trap? Example of mechanically interlocked aromatic [2-5]catenanes built from cyclo[18]carbon

Nikita Fedika, Maksim Kulichenkoa, Dmitriy Steglenkob and Alexander I. Boldyrev*ab
aDepartment of Chemistry and Biochemistry, Utah State University, 0300 Old Main Hill, Logan, UT 84322-0300, USA. E-mail: a.i.boldyrev@usu.edu
bInstitute of Physical and Organic Chemistry, Southern Federal University, Rostov-on-Don 344090, Russia

Received 6th December 2019 , Accepted 28th January 2020

First published on 28th January 2020


The unusual stability of cyclo[18]carbon arising from its aromaticity might be used to provide the kinetic trapping needed in the design of interlocked systems. The kinetic barrier separating the interlocked rings and the chemically bonded complex is about 30 kcal mol−1. In addition, the rings can slide freely, which is a promising property for the design of molecular gears and motors.


The immanent propensity of human nature to seek aesthetically pleasant, symmetric and unusual patterns and topologies has led to many serendipities, especially in the field of organic chemistry. After the centennial legacy of perfectly hexagonal benzene, the 20th century was enlightened by game changing discoveries of new carbon allotropes including fullerene1–3 with perfect soccer ball Ih symmetry and honeycomb-like graphene.4–6 One of the most prominent recent discoveries is the synthesis of cyclo[18]carbon7 (further referred to simply as C18) – a new carbon allotrope, which takes an honoured place among the molecules discovered in 2019, according to the C&EN ranking.8 The ground state structure of C18 has been the topic of many theoretical debates throughout decades.9–15 Experimental characterization of the structure confirmed its unusual polyynic structure belonging to the C9h point group and having alternating single and triple bonds. For a member of the cyclo[4n+2]carbone family satisfying Hückel's 4n+2 rule, this pronounced bond alternation is very surprising. Moreover, it is considered to be doubly aromatic, having 2 mutually orthogonal sets of 9 π-orbitals.14,16 Intuitively, aromaticity is inherently associated with the equalization of bonds due to the formation of a conjugated π-system, however, the cumulenic structure was shown to be a transition state (TS) between the true alternating ground states14 whose structure was finally elucidated experimentally.7 This alternation was rationalized in terms of the second order Jahn–Teller effect.14,16 Interestingly, it was predicted about two decades ago by Saito and co-workers prior to its experimental confirmation.16

The non-trivial ring-shaped structure of the new allotrope alongside its unprecedented stability arising from double aromaticity14 make C18 one of the most promising candidates for mechanically interlocked systems.17–21 Such molecular ensembles are also referred to as kinetically trapped, indicating that such stoichiometry might not be a global minimum on the PES, however the interlocked state is preserved due to the high activation energy required to break the cyclic structures or to bring monomers together to form true chemical bonds. For decades, mechanically interlocked systems, and especially catenanes, have been attracting close attention from the scientific community. The low rotational barriers in some catenanes make them prospective building blocks for molecular electronics,17,22 while their unusual shape might be used to host bioactive molecules and design drug-delivery vectors.23 Moreover, their potential might be realized in molecular sensors and catalysis24 owing to their capability to host and efficiently orientate transition metals.25

For many years, catenanes and other topologies were elusive in real synthesis because of the low probability of formation according to the statistical approach. However, recent advances in polycatenane synthesis, especially the template-directed approach which allows pre-orientation of fragments, opened the gate to experimental obtaining of a wide range of locked systems. This strategy was successfully expanded to poly[n]catenanes and so far the cutting edge example is the targeted synthesis of poly[130]catenane.18 Another impressive example of an all-benzene catenane suggests a new synthetic strategy for catenanes without heteroatoms, which were impossible for a long time.26 Noticeably, this interlocked system is also listed in the prestigious ranking of molecules of 2019.8

Following recent success both in C18 characterization and design of [n]catenanes, in this study we would like to address the possibility of existence of C18-based [n]catenanes and their kinetic stability. For their successful design – either experimental or theoretical – two main criteria should be satisfied. First, to form a true catenane, the structures should interact only “mechanically”, by which we mean that no new chemical (‘electronic’) bonds are formed upon ring closing, thus the structural features of the monomers are mostly preserved. Second, the kinetic barrier separating the mechanically interacting complex and the chemically bonded one should be significant in order to provide the state known as the kinetic trap. The latter condition is necessary for the system to exist because, obviously, catenanes are most likely not the global minima on the potential energy surfaces (PESs), thus only a high activation barrier can preserve their state. While aromaticity is inherently associated with unusual thermodynamic stability of molecules27,28 and clusters,29–35 we aim to show that it could also be used for kinetic trapping, and hence the targeted design of mechanically interlocked systems.

Although the computational study of C18 and its derivatives looks straightforward, it is in fact full of pitfalls. For the selection of the level of theory we would like to refer to the recent study of Sundholm and co-authors in which this topic is discussed exhaustively.14 It is remarkable that many standard time-tested functionals (such as B3LYP or PBE0) fail to reproduce the experimentally observed polyynic geometry of C18, which is explained by insufficient treatment of Hartree–Fock exchange.14 All systems considered in this work were studied at the recommended M06-2X/6-31+G*[thin space (1/6-em)]36,37 level of theory which correctly predicts the polyynic system to be an energy minimum. In addition, to treat the interatomic interactions crucial for mechanical bonds, Grimme's dispersion correction (GD3) was employed in all calculations.38

Let us start with the bonding in the C18 ring, which is a monomer of the suggested [n]catenanes. The bonding picture was deciphered using the AdNDP method,39–45 a flexible tool based on the NBO analysis.46,47 As expected, a frame of 18 σ-bonds was found, which was accomplished by 2 mutually orthogonal sets of 9 π-bonds (Fig. 1). This picture is in full agreement with the experimental observation and CCSD calculations.10,14,16


image file: c9cc09483k-f1.tif
Fig. 1 Bonding pattern of a sole C18 ring. Hereinafter bond lengths are in Å. ON stands for occupation number.

The simplest precursor of poly[n]catenanes is [2]catetane constructed from two C18 rings. This interesting molecular ensemble is also known as a Hopf link.19 The recovered bonding pattern of [2]catetane perfectly resembles the one obtained for the monomer, therefore the first criterion for a mechanical bond is fully satisfied (Fig. 2). Moreover, the ONs remain the same, indicating complete absence of electron transfer. In addition, the distances between two C atoms belonging to different rings are around 3.5 Å, which intuitively means the absence of a chemical bond.


image file: c9cc09483k-f2.tif
Fig. 2 Bonding pattern of [2]catenane formed by two C18 rings. The closest distance between two atoms from different rings is shown in Å.

Some previously reported Hopf links can easily slide along each other.48 This is true in the case of the considered [2]catenane. The calculated barrier of rotation is less than 0.01 kcal mol−1, meaning free rotation of the rings along each other, whereas the energy difference between the rotamers is less than 0.2 kcal mol−1. Obviously, such rotation is perpetually induced by thermal motion at room temperature, which is a valuable property for molecular gears and motors.49–52

While the mechanical character of the inter-ring bond in [2]catenane is confirmed, it is necessary to check whether such a structure is kinetically trapped or not. To investigate this issue we studied the kinetic stability as a reaction pathway between [2]catenane and the chemically bonded complex (Fig. 3). Based on the energetic profile of the reaction we can clearly see that the suggested arrangement is, in fact, kinetically trapped because the kinetic barrier separating the mechanically interacting rings and the complex is 31.1 kcal mol−1. Moreover, the Pretzel-like adduct is less stable than the Hopf link by 21.1 kcal mol−1, since the initial aromaticity is distorted. Both the TS and the adduct exhibit predictable RHF > UHF wavefunction instability owing to their open-shell singlet character. Therefore, the reaction pathway was studied using the broken-symmetry (BS) UDFT-approach which was shown previously to be accurate for large organic molecules.53–55 Further, the biradical open-shell singlet character of the TS adduct was confirmed by the CASSCF(8,8) method. However, one should keep in mind that the barrier value provided is a BS-UDFT estimation and more accurate results might be obtained only by demanding multireference methods combined with dynamic correlation. Moreover, in the absence of any experimental data it is impossible to say how close the DFT results are to the true energetics but, considering the previous successful applications53–55 of the BS-UDFT approach, we believe that the studied pathway should be correct. All relevant computational details are in the ESI. Consideration of a further transformation of the bonded cycle to possibly more stable structures is beyond the scope of our study because it does not provide any additional insight into kinetic stability that might be assessed based on the first (presumably rate-limited) barrier. From the barrier obtained it is already obvious that the system under consideration is kinetically trapped as any catenane should be. To leave the kinetic trap, a significant amount of energy (no less than ∼30 kcal mol−1) has to be provided, which might be explained by the aromatic character of the individual rings. The low rotational barrier implies that the full PES of [2]catenane is extremely complex and accounts for the large number of fully or nearly energetically degenerate rotamers. Therefore, we believe that in addition to the reaction pathway found, many others could coexist, and we expect them to have the same unfavourable energetics.


image file: c9cc09483k-f3.tif
Fig. 3 Energy profile of the formation of the chemical complex from [2]catenane, BS-UM06-2X/6-31+G*.

As for the poly[n]catenanes, we studied systems with up to 5 rings and all of them are revealed to be local minima (Fig. 4A–C). If the latest arrangement is synthesized, it might earn an honoured place among other molecular Olympic rings such as olympicene56 and olympiadane.57


image file: c9cc09483k-f4.tif
Fig. 4 (A–C) [3-5]catenanes, respectively. (D) Borromean rings built from three C18 monomers. The nearest distances between different rings are shown.

The stability trend clearly shows that we should expect longer chains of poly[n]catenanes to be stable as well. It might be interesting to investigate such chains using periodic boundary conditions (PBC) implemented in solid-state codes. However, this approach faces many challenges. As we already discussed, chains are very flexible, therefore plenty of rotamers coexist on the PES. Second, a large unit cell should be considered when employing PBC using exact exchange treatment14 (by pure HF or any hybrid functional). Such an approach demands enormous computational resources without any guarantee that even a good guess would converge to the energy-minimum rotamer.

Notably, so far C18 has been obtained at 5 K, and its stability at higher temperature remains unclear. Previously, it was shown that carbon rings can coalesce, forming fullerenes or other derivatives7,58 at high temperatures, and this might be true for [n]catenanes as well. Hence, we expect that the suggested kinetic trap works at low temperatures. The calculated pathway was discussed in terms of E + ZPE, thus in temperature-independent fashion. To estimate the temperature range in which the kinetic trap works, one needs to perform molecular dynamics simulations which are very challenging for the reasons described above.

Lastly, we would like to consider another peculiar topology known as Borromean rings,19 consisting of three mutually interlocked rings (Fig. 4D). As it turns out, this system is also an energy minimum in which there are no chemical bonds between monomers (Fig. S1, ESI). Remarkably, the C18 rings can adjust their shapes to host other monomers. For example, the individual C18-monomers of the Borromean rings as well as the intermediate rings in poly[3-5]catenanes take an oval-like shape to reduce stereochemical “pressure”. This notable adaptability has great potential in the design of host–guest systems.

To briefly recap, we showed that [2-5]catenanes and Borromean rings built from C18 rings exhibit essential stability when mechanically interlocked. Our conclusions are based on a combined study of chemical bonding and the kinetics of chemical complex formation from mechanically interacting rings. Formation of interlocked systems does not disturb the initial aromaticity of the individual rings, therefore they serve as a kinetic trap with an estimated barrier of about 30 kcal mol−1.

We limited our consideration to [5]catenane but, based on the obtained results, we expect poly[n]catenanes to be stable as well because they are constructed on the same principle. Taking into account the brilliant successes of synthetic approaches to poly[n]catenanes,18 the new report on an all-benzene catenane,26 and the range of prospective applications, we believe that the systems under consideration are not elusive prognostications but promising candidates in supramolecular synthesis.

The work was supported by a Russian Government grant by decree N 220 (agreement No 14.Y26.31.0016) and by the USA National Science Foundation (grant CHEM-1664379). The support and resources from the Center for High Performance Computing at the University of Utah are gratefully acknowledged.

Conflicts of interest

There are no conflicts to declare.

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Footnote

Electronic supplementary information (ESI) available: Discussion of theoretical methods, bonding pattern of Borromean rings and Cartesian coordinates of all structures. See DOI: 10.1039/c9cc09483k

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