Making a Right or Left Choice: Chiral Self-Sorting as a Tool for the

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Making a Right or Left Choice: Chiral Self-Sorting as a Tool for the Formation of Discrete Complex Structures Hanna Jędrzejewska and Agnieszka Szumna* Institute of Organic Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland ABSTRACT: This review discusses chiral self-sortingthe process of choosing an interaction partner with a given chirality from a complex mixture of many possible racemic partners. Chiral self-sorting (also known as chiral self-recognition or chiral selfdiscrimination) is fundamental for creating functional structures in nature and in the world of chemistry because interactions between molecules of the same or the opposite chirality are characterized by different interaction energies and intrinsically different resulting structures. However, due to the similarity between recognition sites of enantiomers and common conformational lability, high fidelity homochiral or heterochiral self-sorting poses a substantial challenge. Chiral self-sorting occurs among natural and synthetic molecules that leads to the amplification of discrete species. The review covers a variety of complex self-assembled structures ranging from aggregates made of natural and racemic peptides and DNA, through artificial functional receptors, macrocyles, and cages to catalytically active metal complexes and helix mimics. The examples involve a plethora of reversible interactions: electrostatic interactions, π−π stacking, hydrogen bonds, coordination bonds, and dynamic covalent bonds. A generalized view of the examples collected from different fields allows us to suggest suitable geometric models that enable a rationalization of the observed experimental preferences and establishment of the rules that can facilitate further design.

CONTENTS 1. Introduction 2. Basic Concepts 2.1. General Self-Sorting 2.2. Chiral Self-Sorting 2.3. Specific Features of Chiral Self-Sorting 3. Models and Methods of Analysis 4. Chiral Self-Sorting Involving Natural Macromolecules 5. Chiral Self-Sorting in Artificial Systems Formed by Electrostatic Interactions 6. Chiral Self-Sorting in Artificial Systems Formed by π−π Stacking 7. Chiral Self-Sorting in Artificial Systems Formed by Hydrogen Bonds 7.1. Peptides 8. Chiral Self-Sorting in Artificial Systems Formed by Dynamic Covalent Bonds 9. Chiral Self-Sorting in Artificial Systems Driven by Coordination Interactions and Chiral Ligands 9.1. Tightly Packed Complexes: Mononuclear, Dinuclear, and Polynuclear 9.2. Macrocycles 9.3. Coordination Cages 10. Chiral Self-Sorting in Artificial Systems Formed by Coordination Bonds with Chirality Generated on a Metal Center 10.1. Mononuclear Complexes 10.2. Dinuclear Helicates © XXXX American Chemical Society

10.3. Trinuclear Helicates 10.4. Cage Complexes 10.5. Cyclic Structures 11. Conclusions Author Information Corresponding Author ORCID Notes Biographies Acknowledgments References

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1. INTRODUCTION Two hands coming together in prayer or in a handshake represent fundamentally different interactions among chiral objects. In the world of molecules “handshake-type” or “prayertype” noncovalent interactions between two chiral molecules are characterized by different interaction energies and fundamentally different resulting structures. Therefore, chiral self-sorting, i.e., the choice of an interaction partner with a given chirality from a complex mixture of many possible partners, is a determinant for the stability and functionality of resulting structures. Interactions involving chiral molecules are engaged in most biologically relevant processes, including formation of double helices, protein−protein and protein−

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DOI: 10.1021/acs.chemrev.6b00745 Chem. Rev. XXXX, XXX, XXX−XXX

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called self-sorting. Naturally, highly selective recognition is always a prerequisite for effective self-sorting. Therefore, for self-assembly of a two-component model system, simple rules based on the relationship between two association constants have been proposed.1 But, in most cases, self-sorting is more complex, since it involves many species, effective concentrations of which are dependent on the presence of other “binders” in the mixture. Even low “cross” association constants, if present in a large variety, may substantially contribute to the final equilibrium. Therefore, self-sorting, as a rule, is more demanding to realize than selective recognition. To distinguish between selective recognition and self-sorting, we suggest determining the ratio between the number of substrates and the number of possible products. If the number of theoretically possible products is greater than or equal to the number of substrates (substrates are defined as all the species that are incorporated in the final structures), the process can be classified as self-sorting (Figure 1b,c). Thus, for a case when

DNA interactions, and interactions of macromolecules with small natural and synthetic molecules (drugs). Except for interactions with non-natural molecules, nature has solved the problem of selecting the right enantiomer via a restriction of the number of possibilities. Thus, chiral interactions in native cellular fluids, despite their complexity, usually involve single enantiomers of natural building blocks (e.g., L-amino acids or Dsugars). Nevertheless, the problem of chiral self-sorting, i.e., the question of how the initial choice of the right enantiomer was made in the prebiotic world to form functional structures by noncovalent interactions, is fundamental for addressing the problem of the origins of homochirality on Earth. This problem becomes relevant when chiral self-sorting couples with catalytic properties, because this situation can result in nonlinear amplification of homochiral molecules from only slightly biased racemic mixtures via autocatalytic processes. Besides the cognitive aspects of chiral self-sorting, the possibility of using artificial building blocks of different chirality in the construction of unknown structural motifs is attractive to chemists as it opens the way toward new functional molecular architectures. These reasons provide significant motivation both for chemists and for biochemists to study chiral self-sorting among natural and synthetic molecules. In this review, we concentrate on chiral self-sorting occurring among natural and synthetic molecules that leads to the amplification of discrete species. We analyze the examples of structures that are formed by noncovalent (hydrogen bonding, π-stacking, coordination, and electrostatic interactions) and reversible covalent interactions. Whenever possible we focus our review on thermodynamically controlled processes. Therefore, we have excluded examples of chiral self-sorting observed only in crystals (formed mainly under kinetically controlled conditions). However, especially for biological macromolecules, even though the interactions are reversible, clear distinction between thermodynamically and kinetically controlled processes for the final structures is not always possible.

2. BASIC CONCEPTS 2.1. General Self-Sorting Figure 1. Processes of (a) selective recognition and (b, c) self-sorting, distinguished by the number of possible products.

General self-sorting has been defined as high-fidelity recognition of self from non-self within complex mixtures.1 This definition is widely accepted in the field, and several reviews on this subject have been published.2−6 Nowadays, with the growing number of examples and with their increasing complexity, the definition is intuitively used in a much wider context than was initially the case and, therefore, it requires some explanation: (a) It is important to stress that the prefix “self” in “selfsorting” means that the process is spontaneous (similarly as in “self-assembly”). Therefore, the term “self-sorting” does not have to refer to interactions between identical molecules, although it may. (b) The expression “within complex mixtures” allows, in many cases, for the intuitive distinction of self-sorting from selfassembly or recognition. For example, let us assume that a receptor is highly selective toward one particular guest. When we use the receptor in a “complex mixture” of many guests and the receptor picks only one guest, this process is intuitively called selective recognition, not self-sorting. On the other hand, when we use two different receptors, each selective for one type of guest within a mixture containing all the components and each receptor picks its best guest, such a process is intuitively

one host and a mixture of n > 1 guests is present, the process is called selective recognition, because the number of possible products (n) is smaller than the number of substrates (n + 1) (Figure 1a). When we have two hosts and n > 1 guests, the process is called self-sorting, because the number of products (2n) is higher than or equal to the number of substrates (n + 2). (c) The term “fidelity” has an unspecified scientific meaning. Intuitively, it is used when a given substrate behaves virtually identically in the complex mixture as it does under conditions where only a single product is possible. This ideal situation corresponds to 100% selectivity. Of course, this is rarely the case, and the border line for fidelity is not established. In principle, any distortion of the statistical distribution can be considered self-sorting. Another issue is how to specify the statistical distribution, especially for an infinite number of possible products. In such a case, if possible, comparison with a reference system devoid of self-sorting ability may be helpful. (d) Reversibility of the product formation during self-sorting is not a requirement by definition, but is often an intuitive B


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Figure 2. Suggested geometric models of chiral dimerization: (a) interactions between surfaces, (b) interactions between corners, (c) interactions between edges, and (d) helicates.

the above discussion on general self-sorting, we define chiral self-sorting as a process that substantially alters the statistic isomeric distribution of formed species and at least one of the components is present as a mixture of enantiomers (either a substrate or a product or both). The process can amplify species composed of the same enantiomers (narcissistic, homochiral self-sorting) or different enantiomers (social, heterochiral self-sorting), or it can proceed between chemically different components. This definition does not impose restrictions on the stability of the products and on the degree of selectivity. Therefore, both covalently and noncovalently formed species can be considered. One should notice that restrictions on stability and selectivity are imposed by the choice of an observation technique and its specific resolution and detection limits: the species must be stable enough and present in a sufficient amount to be observed and distinguished from other species via the given technique.

assumption. If we consider an irreversible process, for example an irreversible chemical reaction, and such a reaction gives only a single product among many possible products, then the process is described as chemo-, regio-, diastereo-, or enantioselective. If such selectivity is achieved in a reversible reaction, it can be called self-sorting. Therefore, reversibility is assumed in self-sorting, which is indeed most often claimed for self-assembled systems formed by reversible noncovalent interactions or dynamic covalent bonds. In an irreversible process, the product distribution is determined by kinetic rates, which are difficult to differentiate at the early stages of formation of a multicomponent product. In such a case effective self-sorting is difficult to realize, due to the lack of errorcorrection mechanisms. (e) There are many types of self-sorting classified by the type of affinity and by the topology of the products. If, within a mixture of substrates, higher affinity for others is shown, the process is called social self-sorting7 (or self-discrimination8). If higher affinity for itself than for others is observed, the process is called narcissistic self-sorting9 (or self-recognition10). Recently, Schalley and co-workers have classified self-sorting systems as integrative or nonintegrative from the type of products formed.11 Nonintegrative self-sorting systems (the most common) are characterized by the formation of a set of discrete complexes, each containing a single recognition center that is occupied by its complementary partner. In integrative systems (much more rare) more than two species are bound in two or more recognition events with positional control and integrated into one global complex.

2.3. Specific Features of Chiral Self-Sorting

General self-sorting, although still not common, is known for organic and inorganic substrates resulting in the amplification of various discrete or infinite species. Prerequisites for highly effective self-sorting are multivalency, complementarity, and relative rigidity that result in high selectivity (measured as a ratio between association constants involving the same components). If the components are sufficiently different, self-sorting can be very effective. However, the presence of competitors possessing similar interaction sites hinders the effectiveness of self-sorting.1 In the light of these experimental observations, the difficulty in effective chiral self-sorting is an obvious consequence. Enantiomers have similar recognition sites and are very often conformationally labile, which allows them to adapt. Therefore, even for a simple two-component

2.2. Chiral Self-Sorting

Chiral self-sorting is one of the types of self-sorting in which chirality is the differentiating factor for selectivity. In the light of C


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between nonequivalent sides in a homochiral arrangement, the building blocks rotate with respect to each other and, in some cases, stacking is still possible (although geometrically less effective, dihedral angle ca. 30°). Formation of heterochiral dimers does not lead to effective stacking interactions, irrespective of the attractive or repulsive interactions between equivalent sides and irrespective of the relative positions of the building blocks. Therefore, homochiral structures are preferred for dimers dominated by surface interactions. If the building blocks form dimers through interactions between their peripheral substituents, the geometric requirements are different. Depending on the dihedral angle between building blocks, the interactions can proceed via corners (dihedral angle ca. 0°, Figure 2b) or edges (dihedral angle ca. 360°/(2n) for Cn symmetric building blocks, Figure 2c). Interactions between corners are mainly observed for selfassembled structures based on metal coordination (a metal ion constitutes the corner). The preference toward a homochiral or a heterochiral structure depends on the nature of additional interactions between the equivalent sides of the ligands (coded by the same color). For repulsive interactions, e.g., between bulky substituents, equivalent sides avoid contact; therefore, a homochiral self-assembled dimer will be preferred. If the interactions between equivalent sides are attractive (e.g., hydrogen bonding or geometric constraints), a heterochiral arrangement will be preferred. Interactions between edges are observed for building blocks that, due to their interaction geometry, require a rotation with respect to each other during dimer formation (dihedral angle up to 360°/(2n), as a result heterochiral dimers of S2n symmetry or homochiral dimers of Dn symmetry are formed, Figure 2c). The geometric result of edge interactions, as compared with corner interactions, is the requirement for more bent building blocks to ensure better contact between edges. The change of the dihedral angle results in a reversal of chiral preferences. Thus, for repulsive interactions between equivalent sides, a heterochiral arrangement is preferred. Helices constitute a topologically different type of selfassembled structures (Figure 2d). Geometrically, they are the most straightforward examples to analyze because self-assembly of heterochiral building blocks with helical shapes would always lead to a collision, irrespective of the number of building blocks. Therefore, homochiral self-sorting always dominates in helical structures. It should be noted that the term “repulsive interactions between equivalent sides” has a broad meaning. It involves the most intuitive steric repulsions, but also hydrogen bonding between, for example, amide groups, since the interactions between equivalent sides of the group are repulsive (N−H··· H−N or CO···OC), even though globally the interaction is attractive.The models presented above are based on simple geometric fits. Self-assembly of molecules is rarely based on one type of interaction or on a well-defined geometric preference. For example, the transition from the surface to corner and then to edge interactions is continuous, since the rotation between building blocks and their interpenetration can vary. At the same time, one should note that the same interactions, e.g., repulsive interactions between equivalent sides, lead to a preference toward homochiral self-sorting for corner interactions, while for edge interactions it should favor a heterochiral structure. This has important consequences, because the intermediate structures may not show chiral self-sorting at all due to

system, selective chiral recognition is a demanding task. With highly similar competitors present in complex mixtures containing enantiomers, effective chiral self-sorting poses a substantial challenge. As the binding sites for enantiomers are similar, other factors such as chirality-dependent deformations of molecular shapes, rigidity of substrates, and topology of the resulting products are determinant for effective self-sorting. Although there are no quantitative measures of these properties, there are intuitive relationships that enable design. Highly twisted molecules, such as those that are based on axially chiral ligands, are predisposed to form self-assembled products of the given handedness. Close packing and strong interactions present in the products are also beneficial, because they induce higher energy barriers between isomeric structures. Some inherently chiral topologies of products, e.g., helices or pinwheel-shaped structures, are also prone to chiral self-sorting. These intuitive rules are now supported by experimental results, as will be discussed later on. This review concentrates on discrete structures; however, due to their helical shape, infinite covalent or supramolecular polymers are susceptible to chiral self-sorting.12−16 This is because formation of infinite helical species is often associated with a cooperative growth mechanism, since directionality and the number of interactions between individual monomer units increases when the first turn of the helix is closed.17 Therefore, infinite helical supramolecular structures are subject to the “sergeants and soldiers” principle (chirality of a mostly achiral system is controlled by very few chiral units) or the “majority rules” (chirality of a system is determined by which isomer is present in a slight excess in a mixture of enantiomers). In discrete systems cooperative effects are usually smaller.

3. MODELS AND METHODS OF ANALYSIS The number of possible discrete shapes that can be generated by chiral self-sorting is infinite. Therefore, a systematic analysis of the geometric relationships for all types of chiral structures is not feasible. Nonetheless, in practice, dimeric structures of various shapes are the ones most commonly encountered and, due to their relative simplicity, usually those most reliably analyzed. Based on experimental observations and on geometric requirements, we propose here a set of models that allows an analysis of the observed chiral self-sorting preferences for the most often observed dimers (Figure 2). The requisite for obtaining a finite structure from two building blocks with the same or different chirality is a head-tohead or helical mode of dimerization (otherwise self-assembly will be infinite). In the construction of models, we considered the following: (1) the geometry of the building blocks, (2) the geometry of the interaction (interactions between corners, edges, or surfaces), (3) the dihedral angle between building blocks, and (4) the type of interaction (repulsive or attractive). Although the models presented here involve building blocks of C3 or C2 symmetry, the conclusions also apply for other chiral building blocks with Cn symmetries. Tight contact between interacting molecules is most often encountered for interactions between surfaces of aromatic compounds (π−π stacking interactions, Figure 2a). In order to introduce chirality to the interaction between surfaces, the surfaces have to be nonplanar. Head-to-head interactions between homochiral building blocks lead to effective stacking of surfaces upon each other (dihedral angle ca. 0°). Such interaction directly stacks the nonequivalent sides of each building block upon each other. For repulsive interactions D


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Figure 3. Racemic DNA crystal structures: (a) B-type DNA duplex, (b) tetrameric G-quadruplex, and (c) four-way DNA junction (L-DNA blue, DDNA green, potassium ions purple, calcium ions yellow, sodium ions pink).

chiral hybridization would open the possibility for applications in diagnostics, sensing, or therapeutics, since enantiomeric oligonucleotides are resistant against nucleolytic degradation and are immunologically passive. The concept of heterochiral pairing has recently been revisited, and pairing only occurs among homochiral antiparallel complementary oligonucleotide strands.25 These results are further supported by an emerging area of racemic DNA crystallography.26 Crystal structures of various racemic DNAs forming duplexes, quadruplexes, and four-way junctions have been studied (Figure 3). Although crystals contained both enantiomers of a given DNA fragment, only homochiral helices were formed (heterochiral pairing was not observed). But in these structures various interhelix interactions between the neighboring helices of the opposite chirality were observed, suggesting that binding of the enantiomeric oligonucleotides to other molecules through their three-dimensional (3D) shape (aptamer type) is still an open possibility. Nucleic acids, especially those with guanine-rich sequences, form not only helical duplexes but also G-quadruplexes (also known as G4-DNA). Four guanines form a hydrogen-bonded square planar guanine tetrad, and two or more guanine tetrads can stack to form a G-quadruplex stabilized by the presence of a metal cation, positioned either in the center or between each pair of the tetrads. The chirality of native G-quadruplexes comes from their carbohydrate parts. Chiral self-sorting during G-quadruplex formation has been studied using D-1 and (D,L)-1 monomeric building blocks (Figure 4a). D-1 in the presence of K+ ions forms a G-quadruplex composed of four tetrads with four K+ ions in the center of each quartet.27 With Ba2+ ions, a G-quadruplex is also formed (Figure 4b) in which Ba2+ cations are located between tetrads. (D,L)-Guanosine with K+ forms a G-quadruplex composed of four tetrads, and each tetrad consists of a mixture of building blocks of different chirality. In contrast, very effective chiral self-sorting has been observed for Ba2+ cations and only homochiral tetrads were observed. The homochiral tetrads further self-assemble into a complex 16component homochiral structure. The authors of the original paper postulate that effective chiral self-sorting originates from strong interactions between components due to high cation charge density and to the location of the Ba2+ ion between two tetrads that leads to preformation of tight dimers. Chiral selfsorting operates at three levels: tetrad formation, quadruplex formation using Ba+ ions (head-to-tail dimerization with a 26° dihedral angle between tetrads), and stacking between two

conflicting trends. Although this complicates the analysis, it is an important cue for the design.

4. CHIRAL SELF-SORTING INVOLVING NATURAL MACROMOLECULES Nature has optimized the problem of chiral self-sorting. On the one hand, it has restricted the number of available enantiomers, for example only L-amino acids are available for protein synthesis, while nucleic acids and most polysaccharides contain only D-sugars. On the other hand, if achiral components or both enantiomers are available, nature has mastered chiral selfsorting and it can perform most of the functions in a highly stereoselective way. For example, the translational apparatus for ribosomal protein synthesis is stereospecific and allows only for the incorporation of L-amino acids into proteins.18,19 D-Amino acids which are found in prokaryotic cell walls and also in some peptides from higher organisms derive exclusively from posttranslational modifications or a ribosome-independent peptide synthesis.20 Chirality-dependent interactions between macromolecules and small molecules can be studied using enantiomers of small molecules (vide infra, for example, the stereospecificity of enzymatic reactions). Nevertheless, studies involving protein−protein, protein−nucleic acid, glycoprotein− glycoprotein, or lectin−carbohydrate interactions between enantiomers of macromolecules are rare. This is due to the lack of effective methods of synthesis of unnatural macromolecules, since genetic modifications or enzymatic methods are obviously excluded. Another reason is the unique complexity of macromolecules that causes the need for simplification of the experimental system rather than addition of new variables (as for using two enantiomers in chiral selfsorting). Therefore, there are only a few examples in the literature that meet the requirements of chiral self-sorting. Most of these concern the formation of infinite aggregates, and often it is not clear if the processes are kinetically or thermodynamically controlled. Although infinite aggregates are beyond the scope of this review, we will here briefly discuss several selected examples (due to the shortage of cases of discrete aggregates involving enantiomers of macromolecules). Formation of DNA helices via the Watson−Crick base pairing of complementary strands (hybridization) is thought to be stereospecific. Many scientists consider this a general principle, and it is also in agreement with the helical model. However, a small number of reports have suggested the possibility of heterochiral DNA hybridization.21−24 HeteroE


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Among peptides, chirality-dependent interactions have been studied for collagen-mimicking peptides. Natural collagen is formed by self-assembly of (glycine-(L)-proline-X)n polypeptide chains (X is any amino acid other than glycine, proline, or hydroxyproline) into left-handed triple helices that further aggregate to form fibers.29 The self-assembly process has been studied using two enantiomers of collagen mimic peptides, ((L)-Pro-(L)-Pro-Gly)10 and ((D)-Pro-(D)-Pro-Gly)10.30 Enantiomerically pure peptides are well soluble at pH 7 in phosphate buffer. Under the same conditions, a mixture containing both enantiomers self-assembles into sheets and precipitates from the buffer solution. Based on these results, supported by TEM, AFM, WAXS and modeling, the authors of the original paper postulate that (a) triple helices form in a homochiral way, because heterochiral helices would require proline residues to adopt highly hindered backbone conformations, but (b) aggregation of triple helices into fibers proceeds more effectively in a heterochiral way, because racemic “screws” can interdigitate and pack more effectively (Figure 5), leading to

Figure 5. Packing of collagen triple helices. (a) Geometric fit of two triple helices of ((L)-Pro-(L)-Pro-Gly)n. (b) Geometric fit of two triple helices: triple helix of ((L)-Pro-(L)-Pro-Gly)n (green) and triple helix of ((D)-Pro-(D)-Pro-Gly)n (blue).

precipitation. Although the resulting aggregates are not discrete and it is difficult to determine if the process is thermodynamically controlled, the current example is an excellent instance of chiral self-sorting of peptides. An interesting example of chirality-driven transformation of peptide secondary structures has been reported for poly(lysine). At pH above 11.1, homochiral poly(L-lysine) has a preference toward formation of an α-helical structure, but it undergoes an α-to-β transition upon an increase in the temperature. A mixture of poly(D-lysine) and poly(L-lysine) undergoes the α-to-β transition at a much lower temperature and precipitates as heterochiral β-sheets, as was originally reported by Fuhrhop and co-workers31 and further studied by Dzwolak at al.32,33 The presence of a second enantiomer causes precipitation of fibers even at the temperature where homochiral samples do not form fibrils at all. These authors have suggested that formation of heterochiral β-sheets is highly preferred, as it drives a transformation of an energetically favored α-helix into β-sheets. Interactions that lead to formation of β-sheets are of interest, because they are crucial to understanding (and preventing) the amyloidogenesis that underlies many neurodegenerative diseases (Alzheimer’s and Parkinson’s diseases, among others). D-Peptides can be considered competitors to natural binding

Figure 4. Self-assembly of guanidine derivatives. (a) Chemical structure of D-1 with the interaction motif. (b) X-ray structure of Gquadruplex formed by D-1 with Ba2+ cations and picrate anions. (c) Chemical structure of (D-2)5. (d) X-ray structure of decamer Cs+(D2)5(L-2)5.

dimers (head-to-head stacking). A different structure has been observed for isoguanosine derivative D-2 in the presence of a Cs+ cation (Figure 4c). D-2 forms hydrogen-bonded pentamers that further dimerize with Cs+ ions positioned between pentamers (Figure 4d).28 Isoguanosine, in contrast to guanosine, forms an intermolecular hydrogen bond between 2′-O in the sugar and 6-NH in the base. This hydrogen bonding is responsible for effective chiral self-sorting during the construction of pentamers, and (D,L)-2 forms only homochiral pinwheel-shaped pentamers (D-2) 5 and ( L-2)5. Further dimerization of pentamers in the presence of Cs+ proceeds preferentially in a heterochiral manner forming a meso diastereoisomer Cs+(D-2)5(L-2)5 in 80% yield (Figure 4d). The dihedral angle between pentamers is 36°, in agreement with S10 symmetry (the repulsive-edge model of dimerization, with repulsive interactions between the peripheral bulky groups). F


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sites, potentially preventing toxic fibril growth. Therefore, chiral self-sorting between enantiomeric peptides during aggregation is widely studied. Whether homochiral interactions are preferred for peptides forming β-sheets is not clear from the occasional reports in the literature, and some results are contradictive. Studies of D- and L-stereoisomers of amyloidogenic Aβ peptides (40 residues) using the radiolabeling technique suggest that deposition of soluble Aβ peptides onto preexisting Aβ aggregates is stereospecific.34 While the Lpeptide is deposited readily onto immobilized L-Aβ aggregates, essentially no association between the D-peptide and L-template has been observed. Similar observations have recently been made for a 44-residue covalent dimer derived from a peptide corresponding to the [20−41]-fragment of human β2-microglobulin (β2m) and the 99-residue full-length protein.35 For both peptides, their racemic mixtures precipitate as homochiral fibers or give amyloids that are composed of largely enantiopure domains; i.e., the peptides undergo a spontaneous Pasteur-like resolution into a mixture of left- and right-handed aggregates (detected by a combination of EPR of nitroxidelabeled constructs and 13C-isotope edited FT-IR spectroscopy). Despite the fact that homochiral self-sorting is postulated during formation of amyloid fibers, the presence of a second enantiomer has a profound effect on the kinetics of fiber growth. For example, it has been found that D-β2m is an efficient inhibitor of L-β2m amyloid growth. Similar observation has also been made for much shorter peptides (only six residues).36 Even though these experimental observations are sometimes considered as being contradictory to homochiral self-sorting, we think that they can be rationalized by the formation of transient heterochiral structures. Due to a structural similarity and conformational lability of peptides, it is likely that many different transient structures are formed during aggregation. These may later disassemble and so are not present in the final aggregates; however, they substantially slow down the process of fibers’ growth. Therefore, these results considerably support the idea of using D-peptides as inhibitors of amyloid propagation. Chirality dependent interactions involving β-sheets are also claimed to be responsible for biasing the stereochemical outcome of a polymerization reaction that leads to polypeptides.37 These results provide plausible explanations for biochirogenesis. During the polymerization reaction involving racemic amino acid derivatives (valine and leucine Ncarboxyanhydrides), amplification of homochiral oligopeptides was observed that increases with the increase of the peptide length. It has been postulated that chiral sorting proceeds mostly at the solid−liquid interface with the aggregated (and precipitated) peptides acting as templates for enantioselective chain elongation. From the above examples of natural macromolecules it is clear that studies on chiral interactions are crucial for understanding basic phenomena such as the origins of homochirality or toxic misfolding of proteins. These cases also illustrate the experimental difficulty (and often ambiguity) of the studies. In fact, it is not known how D-peptides interact with L-amyloid surfaces and whether there are any general rules that might be used in structure-guided design of novel therapeutics based on this strategy. Racemic crystallography of macromolecules provides some insights on modes of chiral interactions,38 but with a reservation that tight packing of molecules in crystal lattices may affect interactions, especially those at surfaces. Studies using artificial models, in addition to

creating new entities, also provide an additional structural and thermodynamic background for the understanding and the rational design of the chirality-dependent processes.

5. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS FORMED BY ELECTROSTATIC INTERACTIONS Electrostatic interactions are considered the strongest noncovalent interactions. Nevertheless, their use in the selfassembly of discrete species is limited by the nondirectional character of electrostatic forces. For chiral self-sorting that by definition requires a high degree of spatial ordering, applications of electrostatic interactions are scarce. In this regard, a unique example of self-assembly driven by electrostatic interactions has been reported for chiral ammonium picrate 3a and 3b (Figure 6a).39 In NMR spectra of R-3a in an acetone

Figure 6. Chiral self-sorting during formation of dimeric salts. (a) Chemical structures of ammonium picrates. (b) X-ray structure of (3a)2 (obtained from rac-3a).

solution, two sets of signals were observed which were assigned to a monomeric and a dimeric ion pair (dimerization constant K = 240 M−1 for 3a). For rac-3a and various ratios of R/S enantiomers, the chemical shifts and the coupling constants were identical, suggesting the formation of homochiral dimers. Sterically hindered salts, e.g., 3c, have much lower dimerization constants. The X-ray structure of rac-3a confirmed the formation of a homochiral dimeric ion pair (Figure 6b). Charge-assisted hydrogen bonds between amino acid derivatives have been used by our group for the construction of dimeric capsules and for studies of their self-sorting abilities. Derivatives 4a and 4b quantitatively form homochiral dimers (L-4a)2 and (L-4b)2 by ionic hydrogen bonds between ammonium and carboxylate groups (Figure 7).40 In a nonpolar environment (such as a chloroform solution), ionic hydrogen bonds are strong and, therefore, the capsule is highly thermodynamically and kinetically stable and can recognize chiral guests.41,42 Mixing of (D-4a)2 and (L-4a)2 in chloroform (in the presence of a polar additive to facilitate exchange) leads to quantitative formation of heterochiral dimer (L-4a)(D-4a), indicating efficient heterochiral self-sorting. This result can be rationalized using crystal structures of (L-4a)2 and (L-4a)(D-4a) and the repulsive-edge (heterochiral) dimerization model (Figure 7c,d). For homochiral dimer (L-4a)2, the side chains of amino acids from the opposite hemispheres point toward each other and thus show steric repulsions between equivalent sides of the edges. In heterochiral dimer (L-4a)(D-4a), the side chains form a propeller-type structure devoid of steric repulsions. The preference toward heterochiral arrangement is most pronounced for amino acids with branched side chains G


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features and often enables highly efficient chiral self-sorting. This propensity has been widely used to produce infinite aggregates by chiral self-sorting.14 It also plays a prominent role in the formation of self-assembled finite structures based on organic building blocks by chiral sorting. The structural requirements for the formation of infinite and finite structures are different. In order to avoid the formation of infinite chiral aggregates, the opposite aromatic faces of the building blocks should not be identical, so that only one face is available for stacking interactions. Therefore, the building blocks should have a dynamically averaged Cn symmetry (with the symmetry axis perpendicular to the interaction aromatic face), but not Dn (which promotes the formation of infinite aggregates). Examples of Cn-symmetric molecules are often found among macrocyclic compounds that contain biaryl or helicene units. Biaryl or helicene units with proper substituents are twisted, and very often they cannot interconvert and therefore they are chiral. Twisting of interacting aromatic surfaces seems to be crucial for effective chiral self-sorting, since such surfaces are the places of the closest contact between molecules and, at the same time, they are the chirality-generating elements. Considering the geometry of such interactions, the dominant mode for dimerization should be based on surface models (Figure 2a); therefore, this should lead to the formation of homochiral dimers. Such a design can be exemplified by macrocycle 5 that is made of three substituted benzo[c]phenanthrene units and shows C3 symmetry with two different π-faces (Figure 8a).44 The differentiation of the faces comes from the nonplanar nature of benzo[c]phenanthrene moieties and from the substitution pattern. Macrocycle (P,P,P)-5 forms dimers in chloroform. Although there are three possible ways of dimerization, the authors of the original paper postulate, based on NMR chemical shifts and crystal structure (Figure 8b), that a dimer formed of two lower rims predominates. In this case, the upper rim of the macrocycle is defined as the face with ester substituents, while the lower rim is hydrogensubstituted. When a racemic mixture of macrocycles (i.e., (P,P,P)-5 and (M,M,M)-5) is used, the dimerization constant Krac is lower than Khomo, that corresponds to an optically pure compound (Krac = 8.8 × 102 M−1 vs Khomo = 1.7 × 103 M−1 both in CHCl3, 25 °C, determined by UV), which may show that homochiral dimerization is thermodynamically preferred. Even though these conclusions are in agreement with the postulated surface dimerization model, considering the complexity of the system (in the number of diastereoisomers) and the limited experimental data, they can only be considered as qualitative. The same group reported the dimerization of larger macrocycles based on differently substituted benzo[c]phenanthrene building blocks (Figure 8c).45 The process was studied using vapor pressure osmometry (VPO). Optically pure compound (M,M,M)-6 forms dimers in chloroform at a much lower concentration (2 mM) than a racemic mixture (M,M,M)6 and (P,P,P)-6 (20 mM) does, suggesting that self-assembly of homochiral dimers is privileged. Exclusive formation of dimers is quite surprising, because the symmetry of (M,M,M)-6 is D3. Thus, the two faces of the macrocycle are identical; therefore, the compound should form infinite aggregates. Formation of dimers can be rationalized either by conformational changes during dimerization (unlikely, considering the rigid structure) or, more likely, by a very low association constant for the formation of higher aggregates (below the detection limit of VPO).

Figure 7. Formation of capsules using charge-assisted hydrogen bonds. (a) Chemical structures of products of the Mannich reaction 4. (b) Xray structure of (L-4a)2 (obtained from optically pure (L-4a)2). (c) Binding motif in homochiral (left) and heterochiral (right) capsules. (d) X-ray structures of (L-4a)2 (left) and (L-4a)(D-4a) (right), top view.

(e.g., valine or isoleucine). In such a case, homochiral capsules are not formed at all. This has far-reaching consequences, requiring a “mutualistic approach” to the synthesis.43 Even though none of the enantiomeric hemispheres (L-4c and D-4c) and homochiral capsules ((L-4c)2 and (L-4c)2) can be synthesized, it is still possible to obtain a hybrid heterochiral capsule (L-4c)(D-4c) due to the mutual benefits originating from chiral self-assembly and the dual irreversible/reversible character of the Mannich reaction.

6. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS FORMED BY π−π STACKING Molecules possessing large aromatic faces are prone to selfassembly by π−π stacking. The advantage of π−π stacking is that it results in a very tight packing of molecules that are usually planar and rigid (aromatic faces are typically positioned 3.0−3.5 Å apart, without a void space between). Therefore, neighboring aromatic rings and even peripheral atoms have well-defined positions and reside in proximity. Such a feature facilitates the prediction of molecular shapes using geometric H


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Figure 8. Chiral self-assembly of molecules via surface interactions between their π-surfaces. Chemical structures of (a) (P,P,P)-5 and (c) (M,M,M)6. (b) X-ray structure of ((P,P,P)-5)2 (obtained from optically pure (P,P,P)-5. (d) Chemical structures of perylene bisimides. (e) X-ray structure of (P-7a)2 (obtained from optically pure P-7a).

the chemical reaction, it initially gave homochiral macrocyclic dimer homo-11 and heterochiral linear dimer hetero-10. However, ultimately the reaction gave the macrocyclic homochiral dimer as the only product. It was postulated that the stacking interactions (much stronger for the homochiral linear byproduct) facilitate the cyclization. As the perylene cores undergo interconversion (at a moderate rate), heterochiral linear byproduct hetero-10 is ultimately interconverted to homochiral byproduct homo-10, which then undergoes cyclization and becomes trapped in the form of homochiral macrocyclic dimer homo-11. Thus, homochiral macrocyclic dimer 11 is kinetically favored and is stable when kept at −20 °C. At ambient temperature it is transformed into a 1:1 mixture of homo-11 and hetero-11 after 24 h. This interesting behavior can be classified as mixed kinetic−thermodynamic chiral selfsorting. Stacking interactions are present only for linear homochiral byproduct homo-10, meaning very efficient thermodynamic chiral self-sorting. Then, the products are kinetically trapped in the form of macrocycle homo-11 (kinetic self-sorting). Apparently, for homo-11 stacking interactions no longer play a crucial role, so chirality is not important. Therefore, the process of isomerization leads to a mixture of homo-11 and hetero-11. A reaction between rac-9 and an analogue devoid of chloride substituents (thus having a different twist angle of the core) leads to efficient chemical self-sorting without the formation of mixed products.49 This highlights the significance of efficient geometric complementarity of surfaces. Other interesting properties of rac-9 that originate from the twist angle, chirality, and aggregation

Dimerization through twisted surfaces has also been observed for perylene bisimides (PBIs) containing substituents at 1, 6, 7, and 12 positions (Figure 8d).46 Atropoisomers of PBIs usually undergo fast interconversion, but the presence of a bridge restricts the interconversion of the perylene core of 8a and shields one of its aromatic faces, leading to a C2 symmetric molecule. 8a forms dimers through interaction of unshielded πsurfaces, as shown by Cotton effects originating from chiral exciton coupling characteristic for π−π dimers. Dimerization constants have been determined by UV/vis as Khomo = 2.8 × 103 M−1 and Krac = 1.5 × 103 M−1 (in a racemic mixture). This allows the calculation of Khetero = 4 × 102 M−1 (n-heptane, 58 °C) and the conclusion that, under reported conditions, homochiral dimers prevail and constitute 93% of the mixture. As expected, dimerization constants and the chiral self-sorting ability depend on the length of the bridges.47 A longer bridge provides higher flexibility of the perylene core, and the interconversion of twisted π-faces becomes faster. This facilitates adaptation of the molecules and more efficient π−π stacking, resulting in an increase in dimerization constants, but a decrease in the efficiency of chiral self-sorting. The X-ray structure of 7a partially confirms the conclusions of the solution studies (Figure 8e). In the crystal of optically pure P-7a, homochiral dimers are observed to form using unshielded πfaces,47 whereas in the crystal of rac-7a, no dimers are found.46 The chirality of the core of the tetrasubstituted PBI group present in rac-9, and its tendency to form homochiral dimers, has been used to direct covalent synthesis of large macrocycles using disulfide bonds (Figure 9).48 When rac-9 was subjected to I


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Figure 9. Macrocyclization reaction driven by chiral self-sorting of rac-9.

properties are the high quantum yield of fluorescence and photostability that enable construction of polymeric fluorescent nanoparticles.50 Another type of imide, naphthalenediimides 12−14, have planar cores and their chirality is introduced at the peripheries and comes from substitution with sulfur-containing substituents (center of chirality) and from N-functionalization with orthosubstituted aryl groups that show hindered rotation about the N−C bond (axial chirality, Figure 10). cis-Atropoisomers show C2 symmetry with the 2-fold axis perpendicular to the aromatic surface, and thus they have one shielded and one exposed πsurface.51 All derivatives, except meso-12 and 13a, form dimers in chloroform. The inability of 13a to form dimers is attributed to stereochemical preferences derived from chirality centers at sulfur atoms. In the most stable conformation of the sulfoxide group, ethyl groups shield one π-surface, while the opposite πsurface is shielded by tert-butyl groups (Figure 10c). Thus, both faces of 13a are shielded. For the other derivatives, preferences during formation of dimers have been studied using concentration-dependent NMR spectra. Based on those data, the group of Matile postulates a preference toward the formation of heterochiral dimers for 12 (70% (P-12)(M-12)), 13b (75% (P-13b)(M-13b)), and 14 (52% (P-14)(M-14)). Xray structures have also revealed that racemates crystallize as head-to-head heterochiral dimers (Figure 10d,e). Studies on

chirality-dependent dimerization of napthalenedimides provide a rationale for the process of active anion transport through lipid bilayers. Dimerization causes deactivation of π-acidic surfaces and inhibits anion transport. In line with this hypothesis, compound 13a, which does not form dimers, shows the best anion transporting abilities. Incorporation of sulfoxides and the resulting increase in π-acidity also make naphthalenediimides derivatives better anion−π catalysts.52 The appropriate absolute configuration of sulfoxides allows high enantio- and diastereoselectivities to be achieved.53 The most classical method to introduce chirality at aromatic cores is to substitute them with peripheral chiral auxiliaries. In order to make such a design effective in chiral self-sorting, interactions between chiral auxiliaries have to be involved, in addition to interactions between planar aromatic surfaces. For example, naphthalenediimides N,N′-disubstituted with cysteines form dynamic combinatorial libraries of dimers, trimers, and tetramers at ratios controlled by template molecules.54 Similar building blocks consisting of two or three naphthalenedimides, such as 15 or 16, form complex chiral knotted structures, as reported by the group of Sanders (Figure 11a).55 Enantiomerically pure building block (L,L,L,L)-15 produces various cyclic oligomers through reversible formation of disulfide bonds. At high salt concentrations, generation of the knotted cyclic trimer ((L,L,L,L)-15)3 (Figure 11b) is amplified J


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Figure 10. (a) Chemical structures of napthalenedimides 12−14. X-ray structures of (b) meso-12, (c) P-13a (crystallized from racemate), (d) (P13b)(M-13b), and (e) (P-13c)(M-13c).

7. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS FORMED BY HYDROGEN BONDS The pool of chiral building blocks available for construction of complex structures using hydrogen bonding is large and diverse. Many building blocks are easily available from natural sources (e.g., carbohydrates, amino acids, chiral carboxylic acids, alcohols, and amines), and have a natural tendency for self-assembly. Among the significant advantages of hydrogen bonds is their directionality that makes them a valuable tool for noncovalent architecture. On the other hand, the above building blocks are often flexible and hydrogen bonds often tolerate quite large variations from perfect geometry, which makes rational design much less precise than it outwardly seems. Hydrogen bonds are susceptible to self-competition and competition from polar solvents; therefore, their application in a polar environment is limited (as opposed to self-assembly based on interactions between π-surfaces). One of the early examples of spectacular chiral self-sorting in hydrogen-bonded systems was reported by the group of Reinhoudt. It was found that, upon addition of barbituric or cyanuric acid to dimelamine calix[4]arenes, nine-component [3 + 6] rosettes are formed by 36 hydrogen bonds and stacking interactions of π-surfaces (Figure 12).57 The rosettes possess supramolecular chirality (none of the components are chiral,

(94%). It was found that only one of the topologically diastereomeric knots is formed. For rac-15, only homochiral trimers were obtained and the resulting knotted structures were the same as for enantiomerically pure 15. Other experiments show that a trefoil knot is kinetically and thermodynamically favored. For a building block containing L-cysteines and D-βalanines, a cyclic dimer was the main product indicating that diastereoisomers have different abilities to self-assemble. The same group also examined self-assembly of 16.56 In water at pH 8, (L,L)-16 forms a library of products with two main components which are cyclic tetrameric knotted structures: a Solomon link (60%, Figure 11c) and a figure eight knot (18%, Figure 11d). In contrast, a racemic mixture of (L,L)-16 and (D,D)-16 behaves differently and self-sorts into a single cyclic tetramer: a meso figure eight knot with an alternating sequence of building blocks (L,L-D,D-L,L-D,D). The meso figure eight knot has sharper NMR signals than homochiral knots, indicating a better defined structure. Based on molecular modeling, it has been also postulated that the meso figure eight knot is more compact and thermodynamically more stable. K


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Figure 11. Formation of knotted structures by interactions between π-surfaces. (a) Chemical structures of monomers (L,L,L,L)-15 and (L,L)-16. (b) Modeled structure of trefoil knot ((L,L,L,L)-15)3. (c) Solomon link. (d) Homochiral figure eight knot.

also comply with the “sergeants and soldiers” rule and amplification of chirality is higher for the use of chiral cyanurates, rather than chiral dimelamines.61 A different geometry of interaction is observed for C2 symmetric glycolurils, for example 19a (Figure 13a).62 The dimers are formed by effective π−π stacking of four aromatic rings of interdigitating molecules and by additional hydrogen bonds. Thus, the surface of interaction is parallel to the main axis of the building blocks and, together with deep interpenetration, results in stereochemical preferences of selfassembly based on the repulsive-edge model. Indeed, in chloroform, rac-19a (or rac-19b) self-sorts to form heterochiral dimers. The heterochiral dimers are stabilized by two hydrogen bonds while the homochiral dimers can form only a single hydrogen bond per dimer. Effective heterochiral self-sorting takes place in a more complex mixture containing four building blocks: rac-19a and rac-19b. Among six possible diastereomeric dimers, only heterochiral dimers (three diastereoisomers) are detected. Thus, the formation of heterodimers is completely diastereoselective, with a preference toward heterochiral selfsorting. A library of C-shaped methylene-bridged glycolurils has been expanded by molecules devoid of symmetry elements (19i).63 Absence of symmetry and presence of a lateral

but the whole assembled system is chiral)58 due to the D3symmetric arrangement of melamine fragments. The rosettes are stable enough to be isolated as single enantiomers with either P or M helicity. When enantiomerically pure chiral dimelamine 17 was used, only a single diastereoisomeric rosette (M,all-R)-(17)3(18)6 was formed (Figure 12a).59 When rosettes (M,all-R)-(17)3(18)6 and (P,all-S)-(17)3(18)6 were mixed, no heterochiral complex was observed. Although the experiment involving racemic building blocks rac-17 with barbituric acid 18 was not reported, the group of Reinhoudt has shown that under similar conditions the rosettes are dynamic and undergo exchange. Therefore, a lack of mixed products permits the assumption that very effective homochiral selfsorting is operating in this complex system. The current broader literature context allows us to analyze this system also from the perspective of two stacked self-assembled π-surfaces with peripheral chirality element interaction. Due to the presence of calixarenes in the corners, the substituents are fixed and the chiral self-sorting can be rationalized via the repulsive-corner model due to steric repulsions between R groups. Although beyond the scope of this review, it is interesting to note that such a system shows a memory of chirality, thanks to its amazing kinetic stability.60 These rosettes L


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Figure 13. Self-assembly of chiral glycolurils. (a) Chemical structures of 19. X-ray structures of (b) heterochiral dimer (19b)2, (c) homochiral dimer (19i)2 (obtained from rac-19i), and (d) heterochiral dimer (19h)2.

Figure 12. Formation of hydrogen-bonded rosettes. (a) Self-assembly of dimelamine calix[4]arene and diethylbarbituric acid. (b) X-ray structure of rosette built from achiral 18 and calix[4]arene dimelamine with R = C4H9 (ref 57).

substituent means that dimers can also adopt different geometries: parallel, skewed, or perpendicular. Unsymmetrically substituted compound rac-19i self-sorts into homochiral dimers in skewed orientation (Figure 13b). Due to different substitution patterns, mixtures of up to four different glycolurils self-sort without formation of any heterodimers. Derivatives rac-19c−rac-19h also form dimers in chloroform solutions.64 They are assigned as heterochiral dimers based on the crystal structure of 19h (Figure 13d). Mixing of rac-19c and rac-19f results in an almost quantitative formation of heterodimers (−)-19c·(+)-19f and (+)-19c·(−)-19f. Helicenes have been known for more than a century and were the first known compounds with helical chirality. The growing number of methods for obtaining enantioenriched helicenes makes them useful in many areas.65,66 [7]Helicenes with two pyridinone rings, e.g., 20a, are C2-symmetric chiral molecules that have complementary hydrogen bonding sites (Figure 14a). Based on the concentration dependence of chemical shifts of rac-20b, it has been postulated that helicenes

Figure 14. Dimerization by hydrogen bonding. (a) Chemical structures of [7]helicenes. (b) X-ray structure of (20c)2 (obtained from rac-20c). (c) Chemical structures of biphenyls 21. X-ray structures of (d) hetetochiral (21a)2 and (e) heterochiral (21b)2.

M


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Figure 15. Organic helicates formed using hydrogen bonds. (a) Chemical structures of carboxylic acids 22 and amidines 23. X-ray structures of (b) 22′a and (c) 22′b (obtained from optically pure (S,S)-22′a and (S,S)-22′b). (d) Chemical structures of ureidopyrimidinones. (e) X-ray structure of ((S,S)-24b)2 (obtained from rac-24b).

20a−20c form hydrogen bonded dimers in chloroform.67 Based on modeling, it has been also postulated that the formed dimers are homochiral. Homochiral dimerization has been confirmed by the X-ray structure of rac-20c (Figure 14b) that shows formation of homochiral dimers within a racemic crystal. Although the experimental evidence for self-sorting in the solution is weak, the hypotheses of the authors of the original paper are rational. Dimerization of helicenes 20a−20c can be explained by the repulsive-corner model, since the directionality of hydrogen bonds leads to repulsive interaction between equivalent sides (e.g., N−H···H−N). A similar model of chiral interactions can be used for the explanation of homochiral dimerization postulated for biphenyls 21a and 21b. The biphenyls with CR2OH substituents in 2,2′ positions exist as atropoisomers due to a high rotation barrier (Figure 14c).68 For rac-21b at −115 °C, two different species were observed, attributed to a monomer and a dimer. DFT calculations show that a homochiral dimer is more stable than a heterochiral dimer. Even though rac-21b was separated into enantiomers by HPLC, comparative studies on enantiomerically pure samples that would have confirmed homochiral dimerization mode have not been performed. Complementary hydrogen bonding is also possible between two properly oriented carboxylic acids or between a carboxylic acid and an amidine (Figure 15).69 Dicarboxylic acid 22a selfassembles into tightly folded dimers in chloroform, and the ratio between the homochiral dimer and the heterochiral dimer

is 2:1.70 Dicarboxylic acid 22b self-sorts in a completely homochiral way. The difference between the behaviors of 22a and 22b has been rationalized by the different twist angles between diphenylethylene groups. Using X-ray crystallography, twist angles of 18 and 48° have been found for 22′a and 22′b, respectively (Figure 15b,c). The calculated energy differences between homochiral and heterochiral dimers confirm the observed preferences. Dicarboxylic acid 22b also forms ion pairs with diamidine 23a. Mixing of amidine (R,R,S,S,R,R)-23a with rac-22b resulted in completely diastereoselective formation of a duplex with one substrate (S,S)-22b. Diastereomeric amidine (R,R,R,R,R,R)-23b showed only moderate diastereoselectivity upon mixing with rac-22b (diastereomeric excess (de) 58%). The current case involves helical folding of two ligands, each having two interaction sites. Therefore, the dimers can be considered organic helicates and homochiral selfsorting can be explained by the helical model. Helical folding and formation of dimers using hydrogen bonds has also been observed for more flexible ligands, e.g., 24 and 25 (Figure 15d). These bisureidopyrimidinone derivatives are highly flexible (due to conformationally labile linkers) with chirality centers also located within the flexible fragments. Ureidopyrimidinone units form hydrogen-bonded self-complementary pairs. Bifunctional derivatives 24 and 25, depending on the concentration, form hydrogen-bonded supramolecular polymers or cyclic oligomers.71,72 At a concentration below 300 mM, derivatives rac-24 and rac-25 exist as dimers in chloroform (measured by N


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Figure 16. Molecular capsules formed by hydrogen bonds. (a) Chemical structure of 26. (b) Calculated structure of C70 ⊂ (26)2. (c) Chemical structures of tris(3-ureidobenzyl)amines 28. (d) Possible regio- and diastereoisomers of 28d−28f. (e) X-ray structure of (28d)2 (obtained from rac28d). (f) Chemical structure of tetraurea calix[4]pyrroles 27. (g) X-ray structure of (27a)2 with guest.

be rationalized using the attractive-edge model, because the binding sides are positioned at the edges and the interactions involve equivalent sides of the edges. Guest-templated dimerization has also been observed for tetraurea calix[4]pyrrole 27a in the presence of 4,4′-dipyridyl N,N′-dioxide as a guest (Figure 16f,g).76 For enantiomerically pure S-27b, a dimeric capsule consists of two diastereomeric hemispheres as a result of the directionality of the hydrogen bonding seam; i.e., the capsule has (S,M)(S,P) stereochemistry.77 When rac-27b was used, in addition to the previously observed signals, signals of a heterochiral capsule consisting of two enantiomeric hemispheres, (S,P)(R,M), were observed. The ratio between heterochiral and homochiral capsules is 2:1 (statistical ratio 1:1), thus suggesting preference toward the heterochiral capsule. This observation is in agreement with the repulsiveedge model suggested in the presence of edge interactions between nonequivalent sides of the edges (due to a directional hydrogen bonding seam). The exchange rate between hemispheres in DCM is low, since in a mixture of (S-27b)2 and (R27b)2 only homodimeric capsules are present. However, in a more competitive environment (DCM/THF 9:1, v:v) only heterodimeric capsules are observed indicating that heterochiral

DOSY). The symmetry of NMR spectra of rac-24a and the Xray structure of rac-24b (Figure 15e) show that the formed dimers are homochiral. For 25, enantiomerically pure products were synthesized. NMR spectra of an enantiomerically pure sample and a racemic sample of 25a were identical, and the critical concentration for formation of random coil polymers was higher for the enantiomerically pure sample (270 mM vs 120 mM for racemate). These experiments are also in agreement with postulated homochiral self-sorting that can be rationalized based on the helical shape of the dimers. Hydrogen bonds have also been used to form chiral porous structures. Ureidopyrimidinone units attached to a cup-shaped cyclotriveratrylene scaffold have been used for the formation of chiral capsules (26, Figure 16a). 26 is chiral due to the inherent chirality of the cyclotriveratrylene cup. Dimeric capsules (26)2 are formed upon complexation of fullerenes C60−C84 in chloroform through a system of 24 hydrogen bonds (Figure 16b).73,74 For rac-26 in the presence of C70, the ratio between homochiral and heterochiral capsules is 7:3.75 For chiral fullerene rac-C76 and rac-26, only one set of signals was observed, suggesting exclusive formation of homochiral complexes. Preferences toward homochiral dimerization can O


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side chains. In the non-hydrogen-bonded pairs (NHB) of antiparallel β-sheets, the side chains gear and clash to a greater extent than those in the hydrogen-bonded pairs (HB) (Figure 17a). The interactions involving side chains within β-sheets have been widely studied for natural homochiral peptides.82−84 For racemic peptides, there are more structural possibilities that come from the formation of antiparallel or parallel β-sheets (regioisomers) and from the chirality of the building blocks (stereoisomers).85 Chiral self-sorting in such β-sheet based systems is determined by the delicate interplay between peptide conformational preferences and by side side-chain···side-chain or side-chain···solvent interactions (attractive or repulsive). To form finite assemblies based on intrinsically infinite βsheets, one has to either block one of the edges of the β-sheets or create a cyclic array (mimicking β-barrels). For pentapeptides 29a−29d, one of the edges is blocked by a selfcomplementary intramolecular hydrogen-bonded motif, while the other edge is available for self-assembly (Figure 18a).86 Dimerization of 29a through antiparallel β-sheet formation was

capsules are indeed more thermodynamically stable. Further studies have shown that upon complexation of different N,N′dioxides capsule (27a)2 has an ability to elongate and widen to accommodate larger guests.78 The directionality of the ureabased binding motif was also used for formation of capsules 28 (Figure 16c). Similar to the previous case, an additional chirality element is generated upon dimerization of tripodal tris(3-ureidobenzyl)amines. This originates from the directionality of the hydrogen-bonded seam.79,80 Therefore, when a single stereogenic center is introduced at one of the arms, as in rac-28d−rac-28f, dimeric capsules can theoretically yield antiperiplanar and synclinal regioisomers (Figure 16d). The antiperiplanar regioisomer yields four stereoisomers (22, due to the presence of the stereogenic center and directionality of the seam), while the synclinal regioisomer can yield eight stereoisomers (23, due to the presence of the stereogenic center, directionality of the seam, and different relative positions of stereogenic centers in the dimer) (Figure 16e). In chloroform, both regioisomers are present. The authors of the original paper postulate that each regioisomer is present in a single diastereomeric heterochiral form (in agreement with the repulsive-edge model). 7.1. Peptides

Peptides have many inherent advantages that make them promising building blocks for the construction of complex systems via chiral self-sorting: they are chiral, diverse, and easily available; they also have a natural tendency to self-assembly. However, their use as supramolecular building blocks has long been neglected. The advantages of peptides have been considered insufficient to outbalance the disadvantages mainly originating from the conformational flexibility of oligopeptides and the consequent low predictability of their 3D structure, especially in complex self-assembled systems. Interactions between peptides involve their backbones, side chains, or nonproteogenic substituents. The use of peptide side chains as the main driving force of self-assembly is still in its infancy. In contrast, peptide backbones have been extensively exploited. In nature, the backbones form two basic secondary structures: αhelices and β-sheets. α-Helices are internally self-complementary, and therefore are unable to be the main driving force of supramolecular self-assembly. Therefore, formation of β-sheets is commonly used to induce or direct self-assembly in artificial systems.81 β-Sheets are subdivided into parallel (Figure 17b)

Figure 17. Binding motifs in natural β-sheets (L-peptides): (a) antiparallel; (b) parallel.

and antiparallel β-sheets (Figure 17a). In natural proteins, antiparallel β-sheets are slightly more stable than parallel βsheets, because hydrogen bonding geometry is more optimal. The antiparallel arrangement is also spatially more feasible for motifs involving single strands, as it requires smaller loops. In a natural β-sheet, the side chains of the amino acids are directed perpendicularly to the sheet and alternate above and below the sheet. Due to the presence of two different types of hydrogenbonded pairs, there are two different types of contacts between

Figure 18. Dimerization of linear peptide derivatives. (a) Homochiral dimerization of 29. (b) Hydrogen bonded dimer of diphenylalanine with a guanidiniocarbonyl pyrrole group. P


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Figure 19. Formation of capsules based on peptides by dynamic covalent chemistry driven by self-assembly. (a) Synthesis of hemispheres based on peptides attached by their N-termini and their inherent chirality. (b) Synthesis of of hemispheres based on peptides attached by their C-termini. Xray structures of (c) (L-33f)(D-33f) and (d) C60 ⊂ (D-35c)2 (obtained from optically pure D-35c).

narcissistic self-sorting process (four homochiral homodimers are formed: [(L,L)-30]2, [(D,D)-30]2, [(L,D)-30]2, and [(D,L)30)]2). The modeled structures of the dimers show that the βsheet motif is highly distorted, mainly due to the pivotal role of a charge-assisted hydrogen bonding motif, and the building blocks are folded around each other in a helical way that explains homochiral self-sorting. A similar derivative containing only a single amino acid residue self-assembles in DMSO into spherical vesicles (diameter 50 nm), which is surprising due the nonamphiphilic nature of these compounds.90,91 Chiral self-sorting, hydrogen-bond driven self-assembly, and dynamic covalent chemistry were used in our group to obtain multicomponent capsules based on peptides. Tetraformylresorcin[4]arene 31 was used as a macrocyclic scaffold, and peptides were attached by their N-termini via the reversible imine formation reaction (Figure 19a).92 All imines 33a−33g form self-assembled dimeric capsules in a highly regioselective and diastereoselective manner by merging of 10 components. Depending on the peptide length, the capsules form in an either homochiral or heterochiral way. When mixtures of peptides with different lengths or different chirality

detected in chloroform. Racemic mixtures of 29b−29d have a pronounced preference toward formation of homochiral dimers (ratios 95.8:4.2−98.5:1.5 at 253 K, as detected by NMR spectra).87 Hydrogen bonding patterns are similar for both homochiral and heterochiral dimers, but for the homochiral dimers the nonpolar side chains of amino acids reside on one side of the β-sheet and therefore additional stabilizing interactions are present. The importance of interactions between side chains has also been confirmed by dimerization studies of a mixture of L-29c and L-29e that show a considerable sequence selectivity.88 Dimerization of dipeptide derivatives has also been reported for diphenylalanie equipped with a guanidiniocarbonyl pyrrole group, 30, in DMSO (Figure 18b).89 The dimerization proceeds by charge-assisted hydrogen bonds. All four stereoisomers of 30 were synthesized: (L,L)-30, (D,D)-30, (L,D)-30, and (D,L)-30, and studied separately and in mixtures. For (L,D)-30, the dimerization constant Kdim was found to be 120 M−1, while for (L,L)-30 Kdim = 3 × 105 M−1, both in DMSO. In a mixture of (L,L)-30, (D,D)-30, (L,D)-30 and (D,L)-30 in principle 10 different dimers can form. It was found that each stereoisomer exclusively interacts with itself in a fully Q


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namically stable and encapsulation of guests is hedged by a high kinetic barrier. Therefore, complexation of proper guests, e.g., fullerenes C60 or C70, does not proceed in the chloroform solution even after heating of (35a)2−(35d)2 and C60 or C70 for 5 days. Quantitative complexation of fullerenes can be realized at the step of capsule formation (during chemical reaction) or, in the solid state, by mechanochemical methods. NMR studies have shown that the chiral cavity has a profound effect on the 13 C NMR spectrum of fullerene C70. Enantiotopic carbon atoms become diastereotopic in the chiral environment and therefore show different chemical shifts.

were used as substrates in the reaction with tetraformylresorcin[4]arene, high fidelity self-sorting was observed based on length and chirality. Only capsules consisting of peptides of the same length and proper chirality (homochiral for di- and tetrapeptides and heterochiral for mono- and tripeptides) were formed. X-ray structures of (L33a)(D-33a), (L-33e)2, and (L-33f)(D-33f) (Figure 19c) show that the binding motifs are fully complementary, engaging all available hydrogen bond donors and acceptors. Complementarity of the binding motifs is the key factor in self-sorting processes, resulting also in the amplification of products composed of substrates with the same lengths. Chiral selfsorting in this case can be rationalized based on the assumption that hydrophobic side chains have to be directed outside the capsules. The experimentally observed chiral preferences ensure the formation of binding motifs with an optimal number of hydrogen bonds. Statistical yields of these capsules are below 1%, indicating that an approach that combines self-assembly with dynamic covalent chemistry could be effective in the formation of complex and well-defined peptidic capsules. Selfassembly can be assisted by considerable structural changes especially for conformationally labile building blocks, as for short peptides. Such changes are energetically costly. Therefore, chiral self-sorting under conditions where the final assembly requires substantial structural rearrangement is more demanding. However, we found that even under such demanding conditions chiral self-sorting can be very effective. For example, self-assembly of 33a to form heterochiral dimer (L-33a)(D-33a) requires a change of inherent chirality of the molecules93 while self-assembly of 33e to form homochiral dimer (L-33e)2 requires a change of the tautomeric form of one of the hemispheres.92 Even though the changes are substantial, in both cases chiral self-sorting proceeds effectively. Effective chiral self-sorting has also been observed for peptides attached to tetraformylresorcin[4]arene via their Ctermini using an acylhydrazone linker (Figure 19b).94 In chloroform acylhydrazones 35a−35d quantitatively form selfassembled homochiral capsules (L-35a)2−(L-35d)2. Different attachment points and longer linkers for the C-attached peptides than for the N-attached peptides result in different binding motifs of the capsules. The binding motifs in acylhydrazone capsules (L-35a)2−(L-35d)2 are not fully complementary, and the strands are grouped pairwise with unmatched amide groups. Such nonperfect complementarity influences the self-sorting abilities of the system. Chiral selfsorting remains very efficient: when racemic mixtures of hydrazides are used in the reaction with tetraformylresorcin[4]arene, only homochiral capsules are formed. On the other hand, when peptides of different lengths are applied, no self-sorting is observed. Thus, for acylhydrazone capsules, chirality plays a critical role in self-sorting, while the length of the peptides does not have an impact. This can be rationalized from only partial complementarity of the binding motifs. For capsule (35b)2 (based on a peptide containing only one amino acid) and for (35c)2 (containing a two amino acid sequence), the conserved binding motif involves only the first amino acid residue in each strand and the motif contains “gaps” between the “pairs of strands” (filled with solvent molecules or with a second amino acid). Therefore, even a longer peptide can fit into the binding motif of a capsule made of shorter peptides by bending and filling the gaps, which therefore leads to ineffective self-sorting based on length. In a chloroform solution, the chiral acylhydrazone capsules are highly kinetically and thermody-

8. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS FORMED BY DYNAMIC COVALENT BONDS Reversibility of reactions enables thermodynamic equilibration and ensures an error-correction mechanism that is a prerequisite for effective self-sorting among covalent structures.95 As has already been exemplified by the dynamic peptidic capsules (Figure 19) and knotted structures (Figure 11), formation of reversible covalent bonds in combination with noncovalent driving forces (stacking interactions or hydrogen bonds in previous cases) is a very effective way to form covalent complex structures via self-sorting. Examples discussed in this section involve compounds that cannot be strictly allocated by the type of inter- or intramolecular interactions responsible for their effective chiral self-sorting. In these cases mostly conformational preferences dictate trends. Under aerobic conditions, dithiol rac-36 (Figure 20) forms a library of trimeric and tetrameric macrocycles as a mixture of

Figure 20. Guest-templated dynamic formation of tetrameric receptor [meso-(R,R-S,S-R,R-S,S)-36]4.

diastereoisomers through reversible disulfide bonds (all in low yields).96 In the presence of tetramethylammonium iodide (TMAI), the formation of [meso-(R,R-S,S-R,R-S,S)-36]4 terameric diastereoisomer is amplified (62% yield). Although the cavity of (36)4 is obviously too large for TMAI, the binding constant for TMAI is quite large, K = 4 × 106 M−1 (pH 9, borate buffer). The authors of the original paper rationalize this outcome by the possibility that [meso-(R,R-S,S-R,R-S,S)-36]4 is the only diastereoisomer which can fold around the guest. In contrast, other ammonium salts amplify the formation of R


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trimers (36)3.97 [(R,R-R,R-S,S)-36]3 and its enantiomer predominantly occur relative to [(R,R-R,R-R,R)-36]3 and its enantiomer, and this ratio can be improved by adding, e.g., trimethyladamantylammonium iodide.98 Oligoamide 37 (Figure 21) exists in helical interconvertable conformations M and P. Under aerobic conditions, the

inclusion. Imine forming reactions were also explored by the group of Mastalerz to form [2 + 3] salicylimine covalent cages 43 using condensation between an inherently chiral C3 symmetric quinacene amine 41 and a bis(salicylaldehyde) 42 (Figure 22c,d).102 Under thermodynamic control a pronounced preference toward homochiral self-sorting was observed (up to 86:14) while heterochiral self-sorting dominates (up to 2:98) under conditions where precipitates were formed during the condensation. This thermodynamic preference can come from conformational properties of bis(salicylimine) linkers, which assume nonplanar C2 symmetric conformations, rendering D3 symmetry of the homochiral cage. Formation of the hetrochiral cage (C3h symmetry) requires Cs symmetry of the linkers, which is only possible by dynamic averaging of two C2 symmetric conformations via rotation about the central single bond. Although torsional barriers for simple biphenyls are quite small, for heterochiral cage 43 three such biphenyls are incorporated as parts of the quite rigid cage, and therefore they can contribute substantially to lowering its stability. A much less known reversible reaction, a zirconocene coupling, was used for formation of chiral macrocyclic products. Zirconocene coupling involves reversible formation of a zirconacyclopentadiene ring from a zirconocene fragment and two alkyne groups, allowing for synthesis of complex structures via a labile C−C bond. The zirconacyclopentadiene ring can be further demetalated, which is an irreversible reaction and thus fixes the products. Reversible zirconocene coupling has been applied for BINOL derivative rac-44a leading to a homochiral dimeric macrocycle 45a in excellent yield (91%, Figure 23a).103 45a was further demetalated to obtain 46a (Figure 23b). For a slightly modified substrate 44b (a dihedral angle between naphthalenes was fixed by a methylene tether), trimeric homochiral macrocycle 45b of C3 symmetry was obtained in a very good yield (80%). All the obtained structures are highly rigid, and the newly formed rigid linker enforces the parallel position of building blocks. These factors are responsible for chiral self-sorting according to the repulsive-corner model. A similar model can also be applied for the rationalization of homochiral self-sorting during formation of macrocycles by the metathesis reaction (Figure 23d).104 The starting materials for the current reaction were not monomers, but homochiral polymers (R-47a)n and (S-47b)n. Under the conditions of the metathesis reaction, the starting materials were depolymerized and transformed into cyclic dimers. Metathesis of a pseudoracemic mixture of polymers gives homochiral dimers. Metathesis of a heterochiral polymer gives the same products. This result is in agreement with the repulsive-corner model (newly formed bonds constitute the corners). Sisco and Moore have calculated the enthalpy difference between homo- and heterochiral cyclic dimers, and surprisingly, they have found it to be too small to explain the diastereoselectivity of the reaction.

Figure 21. Dimerization of foldamer 37. (a) Chemical structure of foldamer 37. (b) X-ray structure of (37)2 (obtained from rac-37).

foldamers form cyclic dimers through disulfide bonds.99 The covalent dimer is composed of two independent helices (double helices are not formed). Even though the helices are quite remote, only homochiral products (P-37)2 and (M-37)2 are obtained, which has been rationalized by conformational preferences of the linkers. Enantiomers (P-37)2 and (M-37)2 are separated by chiral HPLC, and the rate of helix interconversion is much lower in the dimer than in the monomer. For an enantiomerically pure sample, after equilibration of dimers to racemate, heterochiral dimers are not observed, and this further supports thermodynamic preference toward homochiral self-sorting. Conformational requirements also ensure selectivity and chiral-self-sorting during synthesis of macrocycles and cages via imine forming reactions. For example, macrocylic calixsalens all-R-40 have been obtained in a cyclocondensation reaction of (R,R)-1,2-diaminocyclohexane 38 with isophthalic aldehydes 39 (Figure 22a).100 The products have C3 symmetry and their vase-like conformation is stabilized by intramolecular O−H···N hydrogen bonds. Reaction with rac-38 proceeds with highly efficient chiral self-sorting and leads to homochiral all-R-40a− 40d and all-S-40a−40d macrocycles.101 Macrocycles 40a−40d dimerize in a homochiral head-to-head manner in such a way that one aromatic ring of each molecule interdigitates the other macrocycle (Figure 22b). In solid state, (40a)2 and (40c)2 further aggregate in a heterochiral head-to-head manner forming capsules with internal voids capable of solvent

9. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS DRIVEN BY COORDINATION INTERACTIONS AND CHIRAL LIGANDS Coordination bonds are among the most widely used noncovalent interactions for the construction of discrete and functional complex structures, including chiral ones. Coordination bonds are quite strong but, still, in most cases, reversible. A great advantage of coordination bonds over other noncovalent interactions is their directionality, and this results in a precise spatial arrangement of ligands. Upon coordination, S


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Figure 22. Formation of macrocycles and cages via reversible reactions. (a) Imine forming reaction leading to calixsalens 40. (b) X-ray structure of calixsalen (all-R-40a)2 (obtained from rac-40a). (c) Imine forming reaction leading to cage 43. (d) X-ray structure of cage (M,M)-43 (obtained from rac-43).

conformational flexibility of ligands is substantially reduced in the first and also in the second coordination sphere. This can amplify chirality-dependent attractive or repulsive interactions, increasing energetic differences between isomeric structures and therefore leading to effective self-sorting. Thus, the intuitive requirements for effective chiral self-sorting (initially also called ligand self-recognition or self-selection),10,105 i.e., rigidity, a correct coordination number, and legible projection of chirality close to the recognition sites, allow for quite rational design and straightforward realization for coordination complexes. Indeed, the number of examples of chiral selfsorting among coordination complexes is substantially larger than the number of examples among purely organic molecules.

model, due to attractive interaction between equivalent sides of the ligands (coordinating N atoms) and lack of steric hindrance. Coordination spheres of lanthanides incorporate three bidentate ligands. Tris(bidentate) complexes formed using chiral ligand 50 and Y3+, Eu3+, or Er3+ ions in the THF solution have been reported (Figure 25a,b).108 For rac-50, homochiral C3-symmetric complexes Ln(50)3 are formed preferentially (80% for Y3+; for Eu3+ or Er3+ ions only single species are visible in the NMR spectra). X-ray structures of Er(50)3 for (R,R,R) and (R,R,S) complexes show that ligands form pinwheel-type structures and, therefore, for homochiral C3symmetric complexes the space-filling is more effective. The question of whether the distribution of products is thermodynamically or kinetically controlled has also been addressed.109 Thus, the (R,R,R)-(Y(50)3) complex has been equilibrated in the presence of the racemic ligand rac-50 and exchange of ligands has been observed, indicating a thermodynamically controlled process. rac-Y(50)3 has been applied as a catalyst of the polymerization of rac-lactide, leading to highly isotactic (composed of monomers of the same chirality) polymeric chains. Chiral self-sorting has also been observed for tris(bidentate) complexes between racemic BINOL-type ligands rac-51 and Y3+ or Yb3+ and lithium bridges. A single diastereoisomer rac-[Ln(R-51)2(S-51)] has been observed (Figure 25c,d).110 In contrast, the application of sodium-containing bridges leads to exclusive formation of homochiral D3-symmetric complex rac-[Y(R-51)3]. This dependence on the kind of bridging metal has been explained by a larger size of Na+ ion, which prevents attractive interactions between heterochiral BINOL ligands observed for Li+-based complexes.

9.1. Tightly Packed Complexes: Mononuclear, Dinuclear, and Polynuclear

Tight packing of ligands around a single metal center has been reported for bisoxazoline 48 that forms complexes with tetrahedral Zn2+ ions (Figure 24a−c).106 Enantiomerically pure (R,R)-48 gives homochiral complex Zn[(R,R)-48]2. However, application of racemic ligand rac-48 leads exclusively to heterochiral complex Zn[(R,R)-48][(S,S)-48]. The preference toward heterochiral self-sorting can be rationalized by the repulsive-edge model: chirality centers are located at the side panels, and the building blocks are twisted with respect to each other to avoid steric clashes. For less crowded complex Pd(49)2, which exploits a [2.2]paracyclophane scaffold, effective homochiral self-sorting has been observed. (Figure 24d,e).107 This was confirmed by the identity of the NMR spectra of enantiopure and racemic complexes, as well as the lack of formation of pseudoracemic complexes. Formation of a D2-symmetric complex can be explained by the attractive-edge T


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Figure 23. Formation of macrocycles via reversible reactions. (a) Zirconocene coupling reactions of 44a and 44b. X-ray structures of (b) 46a and (c) 45b (zirconocenes omitted, both obtained from racemates). (d) Depolymerization reaction of pseudoracemate (R-47a)n/(S-47b)n.

One of the main inspirations for the synthesis and study of chiral metal complexes is the possibility of using them in asymmetric catalysis. Chiral self-sorting, if present during the formation of a catalytic species, has far-reaching consequences for catalysis, leading to nonlinear correlations between enantiomeric excess (ee) of a catalyst and ee of a product. For example, a positive nonlinear effect has been observed in the reaction of dialkylzinc with aldehydes catalyzed by dinuclear zinc complexes of 3-exo(dimethylamino)isoborneol (DAIB, 52) (Figure 26a).111 Homochiral dimer (S-52)2 is less stable (thermodynamically and kinetically) and more reactive.112 Heterochiral (S-52)(R-52) dimer is more stable and less reactive. Dissociation constants in toluene at 40 °C have been found to be as follows: Khomo = 3 × 10−2 M and Khetero = 1 × 10−5 M.113 As a result of these differences, for low optical purity of DAIB, the “racemic” portion of catalyst loading is effectively trapped and deactivated in the form of the heterochiral dimer. The remaining “optically pure” portion of the catalyst loading catalyzes product formation resulting in an unusually high

enantiomeric excess. The reasons for the higher stability of the heterochiral dimer are not structurally obvious and seem to involve changes of the geometry of the four-membered ring and a transfer of chirality information between remote ligands through zinc-coordinated methyl groups (Figure 26b,c). Crystal structures show that, in the heterochiral dimer, methyl groups are in an anti-relationship, while in the homochiral dimer, a synrelationship between methyl groups is observed. Thus, the repulsive interactions between methyl groups are weaker for a heterochiral complex and the dimerization proceeds according to the repulsive-edge model. Similar preferences have also been reported for zinc complexes of borneol derivatives114 and di-μoxo-titanium salen complex 53 (Figure 26d,e).115 For 53, a heterochiral dinuclear complex (R-53)(S-53) precipitates in the reaction medium (methanol), while the optically pure R-53 exists as catalytically active mononuclear species. As a result, a strong positive nonlinear effect is observed in the asymmetric sulfoxidation reaction catalyzed by 53. Different preferences have been observed for phosphoramidite−Cu+ complexes that U


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attractive-edge model (Figure 27b). Thus, mixing of S-56a and R-56b in acetonitrile results in the exclusive formation of homochiral Ag3(S-56a)2 and Ag3(R-56b)2 complexes, while for a mixture of S-56a and S-56b, in addition to Ag3(S-56a)2 and Ag3(S-56b)2 a new set of signals originating from mixed dimer Ag3(S-56a)(S-56b) is visible. Mixed intermolecular interactions engaging hydrogen bonds or stacking interactions (in addition to coordination bonds) have been reported for the formation of four-component helicates based on ligands 57 and 58 (Figure 28a)119 or for dimers of clothespin-shaped complex 60 (Figure 28b,c).120 In the helicates, the achiral phosphine ligands can be exchanged with chiral diphosphines 59. During the exchange process, diphosphines self-sort in a homochiral way and only complexes with two diphosphines of the same chirality are formed. Among such complexes, one of the distereoisomers is amplified (Pt2(R57)2(58)2(R-59)2, de 19%) due to the presence of the chiral diamidine. Naota and co-workers studied the behavior of clothespin-shaped complex 60 that is chiral due to its twisted structure and the enantiomers can be separated via HPLC. Complex 60 further aggregates in chloroform by π−π stacking, as can be seen in the NMR spectra. Only the racemic complex rac-60 shows a significant concentration dependence of chemical shifts of protons. Dimerization constants are Krac = 26 M−1, Khomo = 3.2 M−1, and Khetero = 98 M−1, indicating a preference toward heterochiral dimers.

Figure 24. (a) Chemical structure of bisoxazoline (R,R)-48. X-ray structures of (b) homodimer Zn[(R,R)-48]2 and (c) heterodimer Zn[(R,R)-48][(S,S)-48]. (d) Chemical structure of ligand 49. (e) Xray structure of Pd(R-49)2 (obtained from optically pure R-49).

9.2. Macrocycles

The principle of an efficient space-filling during a self-assembly process is not satisfied for complexes that contain void spaces, such as macrocycles or cages. From this point of view, efficient chiral self-sorting in void-containing systems is more demanding and, therefore, it may need compensation by a higher rigidity and enhanced complementarity of the ligands. Upon complexation with Pd2+ or Pt2+ ions and bulky dppp coligands (dppp = 1,3-bis(diphenylphosphanyl)propane), semiflexible ligands 61a−61d (Figure 29a−c),121 62 (Figure 29d,e),8 63 (Figure 29f,g),122 and rac-64 (Figure 29h,i)123 form macrocyclic M2L2 complexes. The presence of bulky dppp ligands induces corner-type interactions between chiral ligands. The direction and effectiveness of chiral self-sorting crucially depends on the rigidity and crowding induced by substitution patterns. Ligands rac-61a and rac-61b, with relatively long and flexible linkers, form statistical mixtures of homo- and heterochiral complexes due to adaptation. For more rigid, but not crowded, ligands, e.g., 61c, 62, and 64, heterochiral complexes are preferred, because bulky dppp coligands effectively shield one of the sides of the metal ions positioned in the corners, steric repulsions are absent, and interactions between the equivalent sides of chiral ligands dominate according to the attractive-corner model. For crowded ligands such as 63 and 61d with internal protruding groups, quantitative homochiral self-sorting is observed, because repulsive steric interactions between the equivalent sides of chiral ligands dominate according to the repulsive-corner model. Porphyrins constitute convenient scaffolds for the construction of complex structures, due to their rigid and predictable geometry. Self-assembled porphyrin-based structures are usually formed by exploiting the fifth and sixth coordination sites of a central metal ion and functions incorporated in side groups, usually attached at meso positions. For example, in porphyrins 65a and 65b (Figure 29j,k), the side groups introduce chirality and contain additional coordinating

Figure 25. Formation of tightly packed chiral lanthanide complexes. (a) Chemical structure of alcohol 50 and its complexes. (b) X-ray structure of Y(R-50)3 (obtained from rac-50). (c) Chemical structure of complex Y(R-51)2(S-51)·6THF. (d) X-ray structure of complex Y(R-51)2(S-51), THF omitted for clarity.

are catalysts in many enantioselective reactions.116 In dichloromethane at low temperatures, rac-55 forms binuclear tetrahedral and trigonal complexes with CuI without any selfsorting ability (Figure 26f,g).117 Bulkier ligands, e.g. rac(S,R,R)-54 and rac-(R,R,R)-54, form exclusively homochiral complexes with CuI under similar conditions. Tight packing around metal ions that enable chiral selfsorting has also been observed for C3-symmetric trisoxazoline ligands 56a and 56b (Figure 27a) that form trinuclear D3symmetric complexes Ag3(56)2(NO3)3.118 Attractive coordination interactions between equivalent sides of the ligands, together with a sterically induced twist, are responsible for efficient homochiral self-sorting in the system according to the V


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Figure 26. Chiral self-sorting during formation of catalically active complexes. (a) Equilibrium between homo- and heterochiral 52 dimers. X-ray structures of (b) homochiral dimer (S-52)2 and (c) heterochiral dimer (S-52)(R-52). (d) Chemical structure of R-53. (e) Equilibrium between a monomeric and a dimeric complex. (f) Chemical structure of ligands (R,R,R)-54 and (R,R)-55. (g) Equilibrium between trigonal and tetrahedral complexes.

homochiral complexes, indicating effective homochiral selfsorting in agreement with the repulsive-corner model due to bulky cyclohexyl groups. Zn3(all-R-40c)2 selectively complexes S-sec-butanol in benzene. Solid Zn3(40)2 complexes are porous and are able to adsorb N2, Ar, H2, and CO2. [3 + 3] imine macrocycles 66 containing pyridine coordination groups form differently shaped complexes via sandwiching of lanthanides (Figure 30c).126 Homochiral lanthanide complexes, e.g., [Ln(all-R-66)]3+ in the presence of NaOH, dimerize to give OH-bridged [Ln2(all-R-66)2(μ-OH)2(H2O)2]4+ complexes. [Ln(rac-66)]3+ (a racemic mixture) gives products whose NMR spectra are identical to those of enantiomerically pure dimers, indicating homochiral self-sorting. Further proof of homochiral self-sorting comes from analysis of mixtures containing different lanthanide ions. Although for homochiral complexes (i.e., [Yb(R-66)(NO3)2]+ and [Tm(R-66)(NO3)2]+) homometallic and heterometallic dimers are formed, for heterochiral complexes ([Yb(S-66)(NO3)2]+ and [Tm(R-66)(NO3)2]+) no signals from heterometallic dimers are observed upon addition of NaOH. Bipyridine 67 is a semiflexible chiral ligand which in an acetone solution exists as a mixture of two atropoisomers due to slow rotation around the pyridine−pyridine bond (Figure 30d).127 Optically pure (S,S)-67 upon coordination to (dppp)Pd(OTf)2 forms square [4 + 4] macrocycles, in which the rotation around pyridine−pyridine bonds is locked, and therefore the configuration is fixed. Only a single stereoisomer of D2 symmetry is formed. X-ray structure shows that all alanine substituents are directed away from the cavity and two opposite ligands have (S,S,aR) configuration and two other (S,S,aS) configurations (Figure 30e). Such a preference is dictated by bulky coligands that shield one side of the metal center and thus fix the geometry of pyridine coordinating groups at each corner. Biporphyrin 68 (Figure 30f) has three bonds that show hindered rotation: a porphyrin−porphyrin bond and two porphyrin−imide bonds.128 Therefore, eight stereoisomers are possible (23, as four pairs of enantiomers). In noncoordinating

Figure 27. Homochiral self-sorting of propeller-shaped trisoxazolines. (a) Chemical structures of S-56a and 56b. (b) X-ray structure of Ag3(S-56a)2 (obtained from rac-56a).

atoms.124 In a noncoordinating solvent, racemic 65a (and 65b) dimerizes through coordination of azanorbornene nitrogen to Zn2+ forming a heterochiral dimer, according to the repulsiveedge model (the ligands are rotated by 180° with respect to each other and bulky groups are present at peripheries). In contrast, enantiomerically pure 65a forms poorly defined aggregates in solution, although in the crystal formation a dimer (albeit distorted) has also been detected. Association constants are Khomo = 1.2 × 107 M−1 and Khetero = 1.8 × 108 M−1. In the heterochiral dimer porphyrins are parallel; in the homochiral dimer they are tilted at 14.08°, so spatial arrangement in the heterochiral dimer is favorable. Larger macrocyclic rings can also be formed via chiral selfsorting involving coordination bonds. For example, previously mentioned enantiomerically pure macrocyclic [3 + 3] calixsalenes 40 (Figure 30a), in the presence of zinc acetate form Zn3(40)2 complexes via metal bridging of two macrocycles (Figure 30b).125 Chiral self-sorting during complex formation has been studied using mixtures of macrocycles: allR-40c, all-S-40c, and all-R-40b. In the reaction of macrocycles with the same chirality, i.e., all-R-40c and all-R-40b with Zn(OAc)2, no self-sorting was observed, as proven by MS. A pseudoracemic mixture, i.e., all-S-40c and all-R-40b, gave only W


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Figure 28. Formation of multicomponent interpenetrated complexes. (a) Chemical structure of R-57, 58, R-59, and Pt2(R-57)2(58)2(R-59)2. (b) Chemical structure of anti-60. (c) X-ray structure of the [(+)-60][(−)-60] dimer.

signals and molecular modeling showed that the amplified product is a heterochiral dimer of Cs symmetry. Another bowlshaped molecular skeleton, cyclotriveratrylene (CTV), can also be inherently chiral via a C3-symmetric substitution pattern. Such chiral bowls substituted with coordinating groups, such as pyridine or cyano groups, also form M3L2 coordination cages. Ligands 70a, 70b, 71, and 72 coordinate to Pd2+ ions cisprotected by bulky coligand 74 to form C3v symmetric Pd3(74)3L2 cages in a highly selective heterochiral manner (Figure 31c,d).132 These cages are rigid enough to encapsulate 1,2-dichlorobenzene or iodine in a single-crystal-to-singlecrystal manner. Ligands 75a and 75b form cages in chlorinated solvents by coordination to Pd2+ or Pt2+ ions cis-protected by bulky ligand dppp (Figure 31e,f).133 As compared to Pd2+ complexes, Pt2+ complexes are less labile on the NMR time scale. Although cages based on ligands 75a and 75b seem to be closely related to the cages based on ligands 69−73, unexpectedly, the chiral preference here is toward D3symmetric homochiral diastereoisomers in solution and in the solid state (Figure 31f). On the contrary, in tetrachloroethane at lower temperatures a heterochiral diastereoisomer is also formed for [(dppp)3Pd3(75a)2]6+ (hetero/homo ratio is 56:44), but not for [(dppp)3Pd3(75b)2]6+. We hypothesize that the change in chiral preferences among very similar cages (Pd 3 (69b) 2 6+ and Pd 3 (70a) 2 6+ vs Pd 3 (75a) 2 6 + and Pd3(75b)26+) comes from steric requirements, similar to the previously discussed macrocyclic complexes. Cages Pd3(75a)26+ and Pd3(75b)26+ are small and more crowded. Therefore, in order to avoid close contacts between protruding groups, repulsive interactions dominate and the repulsive-corner model is more proper, in contrast to the attractive-corner model appropriate for less crowded cages. Our rationalization is also

solvents, 68 assembles via orthogonal coordination and forms three entitiestrimer, tetramer, and pentamerwhich were separated by GPC. Each of the assembled species is composed of identical monomers, thus showing homochiral self-sorting. NMR spectra of aggregates made from pure enantiomers are the same as spectra for racemates. The association constant is >1018 M−2 for the trimer, >1027 M−4 for the pentamer, and 2 × 1016 M−3 for the tetramer obtained from an optically pure precursor. We should mention that in the paper the authors of the original paper claim six stereoisomers (three pairs of enantiomers); however, our stereochemical analysis and also their experimental spectra (doubling of intensity and doubling of NMR signals in the fraction for the tetramer) suggest the presence of eight stereoisomers. 9.3. Coordination Cages

Subphthalocyanines are bowl-shaped molecules that can be chiral, provided there is an unsymmetrical substitution pattern (inherent chirality129). Pyridine substituted subphthalocyanines, e.g., 69a and 69b, in the presence of Pd2+ ions (and proper coligands and counterions) form cages of M3L2 stoichiometry (Figure 31a,b).130 For rac-69a, one set of signals was observed in the NMR spectrum and the Torres group postulates the formation of a heterochiral cage of C3h symmetry. Such a heterochiral preference is in agreement with the attractive-corner model, where metal ions constitute the corners and a cis-protecting coligand (ethylenediamine) forces coordination using the equivalent sides of the ligand. Unsymmetrically substituted subphthalocyanine rac-69b can give a mixture of isomeric M3L2 cages.131 Although six diastereoisomers are statistically possible, after equilibration only one diastereoisomer was experimentally observed. The number of NMR X


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Figure 29. Formation of macrocyclic M2L2 complexes. (a) Chemical structures of ligands 61a−61d. X-ray structures of (b) (dppp)2Pt2(M-61b)(P61b) and (c) (dppp)2Pd2(P-61d)2 (obtained from optically pure P-61d). (d) Chemical structure of ligand 62. (e) X-ray structure of (dppp)2Pt2(S62)(R-62). (f) Chemical structure of ligand R-63. (g) X-ray structure of (dppp)2Pd2(63)2 (obtained from rac-63). (h) Chemical structure of ligands 64. (i) X-ray structure of heterochiral (dppp)2Pd2(64)2. (j) Chemical structures of 65. (k) X-ray structure of heterochiral dimer Zn2(65a)2.

rac-70b or rac-73 cages are also formed, but homochiral selfsorting is not so efficient.136 This observation can be indirectly connected to the lower stability of these cages as compared to Pd6(70a)8. Indeed, addition of 70a to Pd6(70b)8 leads to rearrangement and only the Pd6(70a)8 cage is detected. Other examples that show that lack of protecting coligands changes the structure of complexes are ligands 61a and 61d. With dppp as a protecting ligand, 61a and 61d form macrocycles (Figure 29a−c); but with [Pd(CH3CN)4](BF4)2 they form cages Pd6(61d)12(BF4)12 and Pd12(61a)24(BF4)24, respectively (Figure 33b,c).137 The sizes of the cages were estimated using DOSY, DLS, and TEM. The NMR spectra of both aggregates show high symmetry, suggesting homochiral self-sorting. 5,5′-Biporphyrins exist as atropoisomers due to inhibited rotation around the meso−meso single bonds.138 Chiral biporphyrins containing additional side groups, e.g., 77a−77c, form very stable tetrameric boxes through side group coordination (Figure 34; association constants for boxes are

supported by analysis of van der Waals surfaces and the fact that for ligand 63, with bulkier substituents (OMe vs H), heterochiral cages were not observed even at lower temperatures. Tetrameric cages are formed via helical wrapping of rigid bispyridyl-BINOL ligand 76 (Figure 32a) upon complexation with [Pd(CH3CN)4](BF4)2.134 A DOSY experiment and an Xray structure (Figure 32b) both confirmed the formation of a complex of M2(76)4 stoichiometry. NMR spectra of the cages formed from enantiopure and racemic ligands were identical, indicating homochiral self-sorting according to the helical model. When protecting coligands are missing, different types of cages are formed using the same ligands, e.g., cage Pd6(70a)8 (Figure 31c and Figure 33a).135 rac-70a gives single species in DMSO as detected by NMR. X-ray crystallography confirmed that the cages are indeed homochiral and show an unusual geometry of stella octangula (Figure 33a). With racemic ligands Y


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Figure 30. Formation of large macrocyclic complexes via coordination bonds. (a) Chemical structure of calixsalens all-R-40. (b) X-ray structure of Zn3(all-R-40b)2 (obtained from optically pure all-R-40b). (c) Chemical structures of Ln(all-R-66) and its dimeric complex. (d) Equilibrium between diastereoisomers of 67. (e) X-ray structure of heterochiral (dppp)4Pt4(67)4. (f) Chemical structures of porphyrin 68. (g) X-ray structure of pentamer (68out‑out)5 (obtained from optically pure R-68out‑out).

>1025 M−3 in chloroform). The boxes form in a homochiral way. Boxes (77a)4 and (77b)4 that were assembled from racemic biporphyrins were resolved on chiral HPLC. After removal of Zn2+ ions, the resolved complexes yielded enantiomerically pure ligands: biporphyrins 77a and 77b.

benzimidazole and pyridine (Figure 35a,b).139 The ligands exist as racemic atropoisomers, due to inhibited rotation around the single bond between aromatic side units. Upon coordination to Cu2+ ions, three diastereoisomeric complexes are possible. In dichloromethane, 78c preferentially forms an (R,R,Δ) homochiral complex (+ enantiomer: (S,S,Λ)) in 95% yield, (R,S,Δ)/ (S,R,Λ) in 5%, and no (R,R,Λ)/(S,S,Δ) complex at all. An axially chiral BINAM derivative rac-79 (BINAM, 2,2′-bis(diphenylphosphinoamino)-1,1′-binaphthyl), upon complexation with Ni(ClO4)2 or Co(ClO4)2, forms complexes of meridional geometry (Figure 35c,d).140 The complexes are homochiral, i.e., [Ni(R-79)2](ClO4)2 and [Co(R-79)2](ClO4)2 with Λ configuration of metal centers, as established by X-ray crystallography. NMR spectra confirmed the presence of only single diastereoisomers in each case in solution (CD3NO2). With a coordinating counterion, SO42−, R-79 forms different dimeric complexes [Cu(R-79)(μ2-SO4)]2, while rac-79 forms heterochiral complexes (characterized only in solid state, Figure 35e). Chirality at metal centers is common among hexacoordinate complexes due to ease of design. Any bidentate ligand, even a symmetric one, creates chirality at a metal center upon coordination of three such ligands in an octahedral mode. For example, cationic complex 80 and anion 81 (Figure 36) exist as stable Δ and Λ enantiomers. rac-80 and rac-81 interact

10. CHIRAL SELF-SORTING IN ARTIFICIAL SYSTEMS FORMED BY COORDINATION BONDS WITH CHIRALITY GENERATED ON A METAL CENTER The well-defined, nonplanar coordination geometry and kinetic stability of coordination bonds (at least on the time scale of a measurement method) may lead to the generation of a chirality center at a metal atom that constitutes an added variable in the design. In order to fulfill the definition of chiral self-sorting, we will include here only examples where racemic ligands are applied and where, additionally, chirality at the metal atom was generated (nproducts > nsubstrates). Generation of chirality at the metal center which proceeds via enantiomerically pure chiral ligands is considered a diastereoselective reaction, and therefore it will not be discussed here. 10.1. Mononuclear Complexes

Tetrahedral coordination geometry enables the generation of metal’s chirality via coordination of four different ligands or two bidentate ligands, each with nonequivalent binding sites. For example, ligands 78a−78c contain two types of binding sites: Z


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Figure 32. Formation of helical M2L4 cage. (a) Chemical structure of ligand 76. (b) X-ray structure of Pd2(P-76)4 cage (obtained from optically pure P-76).

Figure 33. (a) X-ray structure of homochiral Pd6(70a)8 (obtained from rac-70a). Calculated structures of (b) Pd6(61d)12 and (c) Pd12(61a)24.

only the thermodynamically favored homochiral salts are observed.

Figure 31. Formation of dimeric coordination cages by chiral selfsorting. (a) Chemical structures of subphthalocyanines. (b) Calculated structure of Pd3(69b)2 (X omitted). (c) Chemical structures of ligands P-70−P-73 and 74. (d) X-ray structure of heterochiral [Pd(74)]3(70a)2. (e) Chemical structures of P-75a and M-75b. (f) Xray structure of [(dppp)3Pd3(P-75a)2](OTf)6 (obtained from rac75a).

10.2. Dinuclear Helicates

Helicates formed using coordination bonds constitute a class of compounds among which chiral self-sorting is commonly observed. These helicates are made of multidentate linear ligands helically wrapped around metal centers. The first coordination double helices were synthesized by Lehn,142 and this class of molecules has subsequently been extensively studied.143 The conceptually simplest coordination helicates are constructed using bis(bidentate) ligands coordinating to two metal centers. Depending on the preferred coordination geometry, M2L2 double helicates (for tetrahedral metal centers) or M2L3 triple helicates (for octahedral metal centers) are commonly observed. In fact, some of the previously discussed

via electrostatic interactions forming a (rac-80)(rac-81)2 salt. One set of signals for the bipyridine unit has been observed in CD2Cl2 at 293 K for such a salt, suggesting a dynamic ion pair or a single diastereoisomer.141 Experiments with enantiomerically enriched anions suggest a dynamic equilibrium. At 298 K, homochiral salts (Δ-80)(Δ-81)2 (+ enantiomer: (Λ-80)(Λ81)2) are slightly preferred (72% of the mixture). At 243 K, AA


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Figure 34. Formation of chiral porphyrin box (R-77b)4.

Figure 35. (a) Chemical structures of 78a−78c. (b) X-ray structure of Λ-[Cu(S-78a)2] (obtained from rac-78a). (c) Chemical structure of R79. X-ray structures of (d) [Co(R-79)2](ClO4)2 (obtained from optically pure R-79) and (e) [Cu(R-79)(S-79)(μ2-SO4)]2.

examples also meet certain requirements for helicates, although they were not perceived as such by the authors of original papers. A helical structure implies an inherent tendency toward homochiral self-sorting (Figure 2d), and indeed, experimental results show that chiral self-sorting, if present in the system, leads to preferential formation of homochiral species. There are numerous examples of bis(bidentate) ligands that form helicates, with chirality centers located either at the bridges (ligands 82−84, Figure 37) or in the terminal groups (ligands 85 and 86, Figure 38). Ligands 82a and 82b wrap around tetrahedral Cu+ metal centers to form D2-symmetric

Figure 36. Formation of salts containing ions with chirality at metal centers. Chemical structures of ions 80 and 81.

AB


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Figure 38. Formation of dinuclear helicates by bis(bidentate) ligands with chirality centers located at the terminal parts. (a) Chemical structure of 85. (b) X-ray structure of Cu2(S-85)2 (obtained from optically pure S-85). (c) Chemical structures of 86. (d) X-ray structure of Ag2(S-86a)2 (obtained from optically pure S-86a).

can be electrochemically controlled by reduction/oxidation of metal ions according to the following equation: [CuI2(83)2]2+ → 2[CuII(83)]2+ + 2e−, because the oxidized form (with Cu2+) is mononuclear.146 Ligands 84a and 84b (Figure 37g) form dinuclear halogen-bridged complexes with Co2+ or Ni2+, with the ligands tightly wrapped around metal centers and the valine side chains in proximity.147 Generation of chirality at the metal centers is very efficient and (Λ,Λ)-[Co2(S-84)2Cl2]2+ is formed diastereoselectively (Figure 37h). NMR spectra of the complexes formed from rac-84 and S-84 are identical, indicating efficient homochiral self-sorting. Coordination bonds involving Co2+ ions are labile; therefore, it has been postulated that the complexes are thermodynamically preferred. Chirality centers placed at the terminal parts of bis(bidentate) ligands are also able to induce effective chiral self-sorting, as for pinene-quaterpyridines 85 (Figure 38a) or bis(oxazolyl) pyridine ligands 86. Complexes M2(85)2 with Cu+ and Ag+ ions are formed with the generation of metal chirality (de 99:1, Figure 38b).148 From a racemic mixture of Cu2(S-85)2 and Cu2(R-85)2, a heterochiral component is formed in 11% yield, indicating that homochiral self-sorting dominates. A similar preference has been observed for [Ag2(S86)2](BF4)2 complexes in an acetonitrile solution (Figure 38c,d).149 Helically twisted ligands are efficient in the generation of helical metal complexes. For example, Tröger’s base derivatives 87a−87d form dinuclear homochiral helicates M2L2 with Ag+ and Cu+ (Figure 39a).150 (S,S)-87a gives a (Λ,Λ)-complex, (S,S)-87c gives a (Δ,Δ)-complex, and molecular modeling for 87b and 87d suggests that (S,S)-ligands form (Δ,Δ)complexes. The presence of a flexible linker, as in rac-87e,f, does not prevent formation of discrete M2L2complexes and homochiral (Λ,Λ)-(S,S) and (Δ,Δ)-(R,R) species are formed.151 At a 2:3 M:L ratio, ligands 87b, 87c, 87e, and 87f with Zn2+ yield triple helicates (ESI-MS), but the process is not diastereoselective (NMR). Bis(bidentate) 3,3′-BINOL ligands

Figure 37. Formation of dinuclear helicates by bis(bidentate) ligands with chirality centers located at the bridging parts. (a) Chemical structures of (R,R)-82a and (R,R)-82b. (b) X-ray structure of (Λ,Λ)[{Cu(R,R-82b)}2]2+ (obtained from rac-82b). (c) Chemical structures of (R,R)-83. X-ray structures of (d) Cu2(R-83c)(S-83c), (e) Cu2(R83d)(S-83d), and (f) Cu2(R-83d)2 (obtained from rac-83d). (g) Chemical structures of (R,R)-84. (h) X-ray structure of (Λ,Λ)-[Co2(S84)2Cl2]2+ (obtained from optically pure S-84).

Cu2(82)2 complexes in DMSO (Figure 37a,b).144 Identical NMR spectra of complexes of enantiomerically pure 82b and rac-82b indicate homochiral self-sorting with diastereoselective induction and formation of (Λ,Λ)-[{Cu(R,R-82b)}2]2+ and (Δ,Δ)-[{Cu(S,S-82b)}2]2+ clusters (Figure 37b). The potential for chiral self-sorting seems to come from steric repulsion between bromide atoms, and indeed, for rac-82a that is devoid of such hindrance no chiral self-sorting has been observed. Bis(bidentate) ligands 83 form similar Cu2(83)2 complexes in an acetonitrile solution (Figure 37c−f).145 Homochiral selfsorting in solution has been reported for 83a, 83c, and 83d, but not for 83b (probably due to the presence of competing coordinating atoms). Although in solution the tendency toward homochiral complexation prevails, in solid state both homochiral complexes (Figure 37f) and heterochiral complexes (Figure 37e) are observed. The assembly/disassembly process AC


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Figure 39. Formation of dinuclear helicates by bis(polydentate) ligands with chirality originating from helically twisted ligands. Chemical structures of (a) 87a−87f and (b) 88. (c) X-ray structure of Zn2(S-88a)3 (obtained from optically pure S-88a). (d) Chemical structures of 89a−89c. Calculated structures of (e) Cu2(89a)2 and (f) Fe2(89a)3. (g) Chemical structure of 90. (h) X-ray structure of the (Λ,Λ)-(M-90)3 cage (obtained from optically pure M-90).

Figure 40. Formation of trinuclear helicates and catenanes. (a) Chemical structure of (P,P)-91. (b) X-ray structure of (Δ,Δ,Δ)-[Cu3((P,P)-91)3]6+ (obtained from optically pure (P,P)-91). (c) Chemical structure of 92. (d) X-ray structure of bis[2]catenane formed by (Δ,Δ)-[Ag2((P,P)-90)2] (obtained from rac-90).

with Zn2+ and Fe2+ in acetonitrile/dichloromethane.152 Within each complex, both metal centers have the same configuration

88a−88c (Figure 39b) form discrete homochiral M2(88)2 double helicates with Cu+and Ag+ and M2(88)3 triple helices AD


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Figure 41. Octahedral cage complexes. (a) Chemical structures of 93a and 93b. (b) X-ray structure of (Λ,Λ,Λ,Λ)-[Ga4(S-93a)6]12− (obtained from optically pure S-93). (c) Chemical structures of 94 and 95. (d) Calculated model of Eu4(94)6. (e) X-ray structure of Eu4(R-95)4 (obtained from optically pure R-95).

is formed in a completely reversible process (Figure 40c,d). Under such conditions, catenation also proceeds for the previously reported bis(bidentate) ligand 90. Homochiral selfsorting is observed for the helicate and for the catenane.

and only single diastereoisomers are formed. ROESY NMR spectra and X-ray crystallography have shown the formation of (Δ,Δ)-Zn2(S-88)3 and (Δ,Δ)-Ag2(S-88)2 complexes (Figure 39c). Cu+ complexes show fast ligand exchange, whereas Ag+ and Zn2+ show no exchange (examined by ESI-MS using pseudoracemic ligands 88b and 88c). Bis(bidentate) 6,6′substituted BINOL ligands 89a−89c also form double and triple helicates with Ag+, Cu+, Fe2+, and Zn2+ ions (Figure 39d− g).153 Well-defined complexes are only observed for Ag+, while the other complexes are highly dynamic. CD spectra show that Cu+, Ag+, and Fe2+ helicates have the same configuration (Δ,Δ) for R-89. Bis(bidentate) phenantrolines 90 generate dinuclear triple helicates with Zn2+ (Figure 39g,h).154 Racemic 90 only forms homochiral (Λ,Λ)-(M-90)3 and (Δ,Δ)-(P-90)3 cages with internal cavities able to accommodate small molecules, e.g., 1,3-dioxane and 1,4-dioxane.

10.4. Cage Complexes

Hexacoordinate octahedral geometry is also observed for Ga3+ ions forming Ga4(93a)612− clusters (Figure 41a,b).157 For S93a, only one set of signals is observed in the NMR spectrum in D2O, and for rac-93a the spectrum is identical. X-ray structure indicates that homochiral T-symmetric clusters (Λ,Λ,Λ,Λ)-[Ga4(S-93a)6]12− with all hydrophobic methyl groups buried inside the cavity are formed. Ligand 93b, with a longer spacer, forms Ga2(93b)3 complexes, and the process is not diastereoselective. Bis(tridentate) ligand 94 and tris(tridentate) ligand 95 (Figure 41c) form cage complexes, Eu4(94)612+ and Eu4(95)412+ respectively, via octahedral coordination of Eu3+ ions.158 rac-94 forms a dynamic statistical mixture of diastereomeric complexes, while rac-95 undergoes homochiral self-sorting in acetonitrile, giving a single diastereoisomer. An X-ray structure analysis has determined a (Λ,Λ,Λ,Λ) configuration of [Eu4(R-95)4]12+ (Figure 41e). A self-sorting process has also been observed between ligands R94 and R-95 (NMR COSY, DOSY, ESI-MS).

10.3. Trinuclear Helicates

By increasing the length of a ligand and the number of coordination sites longer helicates are formed. Tris(bidentate) ligand 91 forms trinuclear double helicates [Ag3(91)2]3+ and [Cu 3 (91) 2 ] 3+ and triple helicates [Fe 3 (91) 3 ] 6+ and [Zn3(91)3]6+ (Figure 40a,b).155 rac-91 shows complete homochiral self-sorting with the (Λ,Λ,Λ)-(M,M)-91 diastereoisomer preferred, as suggested by DFT calculations. Ligand 92 forms double helicates (Δ,Δ,Δ)-[Ag3((P,P,P,P)-92)2] in CD2Cl2.156 However, in acetonitrile a bis[2]catenane structure

10.5. Cyclic Structures

From the examples above, it is clear that properly designed bis(polydentate) ligands tend to form dinuclear double or triple AE


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activity on chirality-dependent relationships in multicomponent mixtures. The great potential of chiral self-sorting has only started to be recognized in many areas. In the area of organic synthesis, the advantages are immediately visible in the design of novel functional asymmetric catalysts, as chiral self-sorting induces nonlinear catalytic effects that cannot be achieved in any other way. More advantages in chemical synthesis can be appreciated if chiral self-sorting is present at the early stages of chemical reactions (transition structures or transition states) and thus controls the reaction outcome, for example during cyclization reactions. In biological sciences, chirality-driven self-assembly has revealed its potential in therapies based on D-peptides, especially in neurodegenerative diseases, where aggregation processes are of paramount significance. The advantages of chiral self-sorting have also been recognized in the design of active anion transporters, modulation of fluorescence, and induction of chiral memory effects. However, many areas are still in their infancy, for example, the strengths of a racemic nucleic acid world and dynamic aspects of chiral self-sorting. Switchable dynamic and metastable structures, which will be able to perform tasks on demand, especially in the fields of dynamic asymmetric synthesis and in the construction of nanodevices with chirality-driven unidirectional motion, are still awaiting exploration.

helicates. Other discrete architectures are much less common for such ligands. A unique example in this regard is the P[Cu6((−)-96)6]6+ macrocyclic complex that is made of a bis(bidentate) ligand (−)-96 via the formation of a circular helix with Λ configuration of metal centers (Figure 42).159 For

Figure 42. Formation of cyclic structures. (a) Chemical structure of (−)-96. (b) X-ray structure of [Cu6((−)-96)6]6+ (obtained from optically pure (−)-96).

this macrocycle, identical NMR spectra of complexes of (−)-96 and rac-96 indicate homochiral self-sorting, while meso-96 with Cu+ ions precipitates as a coordination polymer.

AUTHOR INFORMATION

11. CONCLUSIONS This review encompasses examples of amplification of discrete species by thermodynamically controlled chiral self-sorting. Within this scope, we assume that the review is comprehensive. Although the number of examples is not large and they are quite scattered across biochemical, organic, and inorganic areas, they seem to be sufficiently illustrative for a first integrative view on the prerequisites of efficient chiral self-sorting, the significance of the process, and prospects for the future. The first conclusion is that chiral self-sorting can produce a variety of structures, ranging from aggregated peptides through artificial organic receptors to functional inorganic complexes and helix mimics. In order to proceed effectively, the building blocks should explicitly expose their chirality. In this regard, “twisted” building blocks composed of axially chiral fragments are unrivaled. In order to take full advantage of “twisting”, such building blocks need to have proper rigidity: not too flexible (otherwise the advantages of chiral shape will be lost in the conformational multifariousness), but also not too rigid, because the match between building blocks is rarely perfect and often requires slight adjustments. Many examples show that semirigid building blocks with pronounced conformational preferences are highly useful in thermodynamically driven systems, because differences in the conformational energy of a single molecule can be significantly amplified at the supramolecular level, while still allowing for some adaptations. For observed amplification effects, self-assembled discrete structures lay in-between infinite supramolecular polymers and bimolecular recognition events. Spectacular cooperative mechanisms leading to nonlinear effects, as in the case of infinite assemblies, are not so profound for finite assemblies. However, surprising effectiveness and unexpected selectivity are not uncommon for finite structures and new motifs are often generated upon introduction of chirality as an added variable. These features make chiral self-sorting a promising tool for the generation of new complex structures and also an area of intense research

Corresponding Author

*E-mail: [email protected]. ORCID

Agnieszka Szumna: 0000-0003-3869-1321 Notes

The authors declare no competing financial interest. Biographies Hanna Jed̨ rzejewska is a Ph.D. student in the research group of Agnieszka Szumna. She received a M.Sc. in biotechnology from Warsaw University of Technology in 2012. Her research focuses on peptidic capsules and self-sorting processes. Agnieszka Szumna is an associate professor in the Institute of Organic Chemistry, Polish Academy of Sciences, Warsaw, Poland. She received her M.Sc. in chemistry (crystallography) from Warsaw University (1996) and Ph.D. in organic chemistry (supramolecular chemistry) under the supervision of Prof. Janusz Jurczak from the Institute of Organic Chemistry, Polish Academy of Sciences (2001). She was a postdoctoral fellow with Prof. Jerry L. Atwood at University of Missouri, Columbia, USA. In 2010 she received a habilitation (awarded as an outstanding habilitation by the Prime Minister and the III Department of Polish Academy of Sciences). Since 2012, she has worked as an assistant professor at the Institute of Organic Chemistry, where she leads the laboratory for Molecular Recognition. Her research focuses on various aspects of molecular recognition with a special emphasis on chiral recognition and separation, new types of chirality, dynamic covalent chemistry, encapsulation, reactivity, and dynamics in confined spaces.

ACKNOWLEDGMENTS A.S. acknowledges the financial support of the National Science CenterPoland (Grant 2013/09/B/ST5/01026). H.J. was supported by the National Science CenterPoland (Grant 2014/15/N/ST5/02019). AF


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