Engineering crystals of dendritic moleculesOleg Lukina,b,1, Dirk Schuberta, Claudia M. Mullera, W. Bernd Schweizerc, Volker Gramlicha, Julian Schneidera,Grygoriy Dolgonosd, and Alexander Shivanyukb

aInstitute of Polymers, Department of Materials, HCI G527, and cOrganic Chemistry Laboratory, HCI G301, Eidgenossische Technische Hochschule, 8093Zurich, Switzerland; bNational Taras Shevchenko University, Volodymyrska Street 64, Kiev 01033, Ukraine; and dBremen Center for Computational MaterialsScience (BCCMS), Bremen University, Am Fallturm 1, 28359 Bremen, Germany

Communicated by Julius Rebek, Jr., The Scripps Research Institute, La Jolla, CA, April 22, 2009 (received for review January 20, 2009)

A detailed single-crystal X-ray study of conformationally flexiblesulfonimide-based dendritic molecules with systematically variedmolecular architectures was undertaken. Thirteen crystal struc-tures reported in this work include 9 structures of the second-generation dendritic sulfonimides decorated with different arylgroups, 2 compounds bearing branches of both second and firstgeneration, and 2 representatives of the first generation. Analysisof the packing patterns of 9 compounds bearing second-genera-tion branches shows that despite their lack of strong directivefunctional groups there is a repeatedly reproduced intermolecularinteraction mode consisting in an anchor-type packing of comple-mentary second-generation branches of neighbouring molecules.The observed interaction tolerates a wide range of substituents inmeta- and para-positions of the peripheral arylsulfonyl rings.Quantum chemical calculations of the molecule-molecule interac-tion energies agree at the qualitative level with the packingpreferences found in the crystalline state. The calculations cantherefore be used as a tool to rationalize and predict molecularstructures with commensurate and non-commensurate branchesfor programming of different packing modes in crystal.

dendrimers � single-crystal X-ray � sulfonimides � supramolecular chemistry

Revealing the interplay of noncovalent forces that directprocesses of self-assembly and self-organization has been

objective of numerous studies (1–4). This is central for the designand then the targeted synthesis of molecules capable of assem-bling into predefined supramolecular structures of practicalsignificance. Although there are many examples in which theknowledge about the noncovalent interactions helped to arriveat predetermined complex molecular architectures (5, 6), theserendipity contributes to a large extent to supramoleculardesign. Once a new fascinating supramolecular structure isdiscovered, it is often difficult to decode the underlying princi-ples of its assembly. In this context the crystallization of organicmolecules is a specifically complicated case that remains poorlyunderstood. Although it is now often possible with the aid ofcomputations to predict a most favorable intermolecular inter-action between molecules there is no guarantee that this par-ticular intermolecular contact will be found in the crystalstructure. Attempts at the rational design of organic crystalsevolved into a nowadays well-established field of crystal engi-neering (7–11) that aims at general rules for crystal structurecontrol. For the time being the field of crystal engineering hasgenerated some knowledge that often helps to design organiccrystals with desired properties. The main recipe is to useso-called ‘‘tectons’’ (12), which are small molecules with well-defined shape and strong directive functional groups, such ashydrogen-bonding units and metal-coordinating sites (13, 14). Incase reproducible trends in crystal packing for a given group ofcompounds are observed the molecules are usually syntheticallymodified in a systematic way to influence the crystal structure.

In this article, we report the first systematic structural study offlexible branched molecules lacking directive functionalities.This study relies on the single-crystal X-ray analyses of 13structures of increasing branched complexity and is accompa-nied by theoretical calculations. The selection of objects for the

present study was stimulated by both basic and applicativereasons. Indeed, the majority of dendritic molecules have low orno tendency to form crystals. There are only a few papersreporting single-crystal X-ray analysis of some dendritic struc-tures of first (15–28) and second (29–34) generations. Althoughthese results are highly interesting, there is still the lack of apremeditated structural study of dendritic molecules, whichmight shed some light on the factors controlling self-assembly ofthese flexible architectures. Dendritic molecules capable ofself-assembly have potential applications as liquid crystalline andelectronic materials (35–40). It is therefore important to be ableto deliberately construct covalent and supramolecular architec-tures involving dendritic species. Recently, we demonstrated thatsulfonimide-based dendrimers (41–43) can be precisely tailoredwith respect to their structural details enabling programmedanalysis of the influence of small structural variations on anumber of their physicochemical properties. The sulfonimide-based dendritic molecules are mainly crystalline solids withrelatively high melting points, which prompted us to undertakea detailed study toward growing single crystals suitable for theX-ray analysis.

Results and DiscussionBranched sulfonimides, such as 1-6 depicted in Scheme 1, bearmultiple aromatic rings held together by sulfonimide branchingpoints. The synthetic methodology affording this type of struc-tures has already been reported by us (41) and synthetic proce-dures for the new compounds are collected in the SI.

Crystals suitable for single-crystal X-ray analyses were grownfrom methanol (compounds 1 and 2, 2 to 3 days, slow evapora-tion), dichloromethane/methanol (compounds 3, 5a, 5b, 5d, 5e,5g and 6a, 2 weeks, slow evaporation; compound 4, 5 days, vapordiffusion), dichloromethane/methanol/acetonitrile (compounds5c and 5f, 3 to 4 days, slow evaporation), and chloroform(compound 6b, 4 weeks, slow evaporation). Following the orderof increase of molecular complexity, Figs. 1–6 depict the single-crystal X-ray structures of compounds 1–6 focusing on theirpacking in crystal.

Parallel �-stacking involving 2-naphthyl groups with interpla-nar distances of 3.5 Å is present in crystal structures of simplesulfonimides 1 and 2 (Fig. 1). This type of intermolecularinteraction is often observed in crystal structures of differentaromatic compounds (1) and in some cases is regarded as adirectional interaction, e.g., in crystal structures involving com-bination of aromatic and perfluoroaromatic rings (44) and othercombinations of electron-rich and electron-deficient aromaticcompounds (45). The directional role of the parallel �-stacking

Author contributions: O.L. designed research; O.L., D.S., C.M.M., W.B.S., V.G., J.S., G.D., andA.S. performed research; O.L. analyzed data; and O.L. wrote the paper.

The authors declare no conflict of interest.

Data deposition: The atomic coordinates have been deposited in the Cambridge StructuralDatabase, Cambridge Crystallographic Data Centre, Cambridge CB2 1EZ, United Kingdom(CSD reference nos. 641741–641747 and 685214–685219).

1To whom correspondence should be addressed. E-mail: o.lukin@ukrorgsynth.com.

This article contains supporting information online at www.pnas.org/cgi/content/full/0904264106/DCSupplemental.

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in the crystal formation in 1 and 2 is questionable because, as willbe shown below, the �-stacking is not observed in largerdendritic sulfonimides. It is rather reasonable to assume that theparallel arrangements of the aromatic rings in crystals of 1 and2 favor more compact packing and, consequently, the gain incohesion energy.

Compounds 3 and 4 are the simplest expanded branchedanalogues of 1 and 2, respectively. As shown in Fig. 2, the packingof molecules of 3 and 4 in crystal involves the intermolecularanchor-type overlap of the complementary branches (shown inthe dotted circles in Fig. 2 and schematically illustrated in Fig. 3).Additionally, like in the case of compounds 1 and 2, the parallel�-stacking involving naphthalene rings is also observed incrystals of 3 and 4. A detailed inspection of the intermolecular

overlap of the complementary branches (Fig. 3) in crystals of 3and 4 reveals that arylsulfonyl and p-sulfonimidobenzenesulfo-nyl rings in both structures are not parallel, which would be aprerequisite for an effective �-�-stacking. Instead, the rings areconsiderably tilted (the angle between the aromatic rings in 4 is40°) that makes the intermolecular contact very compact andsecures the efficient space filling.

Symmetrical 5a–5e bearing small substituent in para or metapositions of the peripheral arylsulfonyl rings are representativesof the next branching event. Figs. 4 and 5 show the interactionsof molecular pairs in crystals of compounds 5a–5c and 5d,e,respectively. Like in case of compounds 3 and 4, the mostfrequently observed molecule-molecule contacts in crystal struc-tures of 5a–5c and 5d,e involve overlapping of their complemen-tary branches. Notably, the molecular structure of 5e (Fig. 5Middle) has the unusual conformation of the central sulfonimidebranching point differing significantly from those found in allother dendritic sulfonimides. This noticeable conformationalchange at the central sulfonimide unit in 5e reflects an ease ofgeometric adjustability of branched oligosulfonimides to the

Scheme 1. It depicts structural formulae of compounds 1–6.

Fig. 1. Fragments of packing of 1 (A) and 2 (B) in crystal.

Fig. 2. Fragment of packing of 3. (Upper) and 4 (Lower) in crystal. Dottedcircles denote the characteristic intermolecular contacts.

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crystal packing effects. Noteworthy, the unusual molecularconformation of 5e does not influence the characteristic inter-molecular contact between the complementary branches (Fig. 5Bottom), as in the case of 3, 4, and 5a–5d.

Fig. 6 Top and Middle show packing of molecular pairs ofsecond-generation unsymmetrical dendritic sulfonimides, so-called Janus-dendrimers (46, 47) 6a and 6b in crystal. Similarlyto the above discussed symmetrical second-generation dendriticsulfonimides the intermolecular interaction consists of the over-lapped second-generation branches. An interesting difference inthe crystal packing of 6a and 6b is that the unlike branches of theformer and the like ones of the latter are involved in theirintermolecular contacts. The intermolecular contacts involved inpacking of 6b in crystal are only the interactions of the com-plementary branches. As shown in Fig. 6 Bottom, this leads to theformation of channel-like structure with channels occupied bysolvent molecules.

Considerable sizes and matching shapes of the second-generation branches participating in the molecular packing of5a–5e and 6a,b seemingly make the main contribution to theoverall cohesion energy in their crystals. This type of intermo-lecular interaction, schematically depicted in Fig. 3, reproduciblyobserved in the 9 above mentioned crystal structures does notdepend on the solvents that are either used for crystallization orpresent in the crystals. It therefore depends on the primarystructure of the dendrimer.

Although the rationalization of crystal structures on the basisof intermolecular interactions in molecular pairs is a ratherdangerous venture, the repeated occurrence of the packingmode depicted in Fig. 3 in the 9 crystal structures prompted usto carry out a theoretical analysis of this type of interaction. Inview of the recent comprehensive report by Dunitz and Gavez-zotti (48) stressing the nonlocalized nature of intermolecularinteractions, the following discussion of structural effects on thepacking patterns in crystal structures of compounds 1–6 lackingstrong directive sites relies on theoretically assessed molecule-molecule interaction energies rather than contacts betweenpoint atoms. The X-ray structural geometries were used asstarting points in the full-energy minimization with a density-functional-derived self-consistent-charge density-functionaltight-binding with dispersion term (SCC-DFTB-D) method (49,50). The interaction energies were obtained by subtracting thesum of total energies of monomers from the total energy of thecorresponding bimolecular complex. The calculations revealedthat the interaction energy is sensitive to the nature of theoverlapping branches. For instance, interaction energy calcu-lated for the homodimeric complex of the interacting pair of4-nitrophenyl-decorated branches, as in 4, is lower than that ofthe homodimeric complex of 2-naphthyl-decorated branches, asin 3, 5e, and 6b (�27.3 vs. �23.8 kcal/mol, respectively). Theheterodimeric complex involving both 2-naphthyl- and 4-nitro-phenyl-decorated branches, as in 6a, is the most stable in thistriad (�28.0 kcal/mol). This agrees with the experimentallyobserved interaction of the unlike branches in the crystal

structure of 6a. Interestingly, the calculated interaction energiesof the intermolecular parallel �-stacking involving 2-naphthylgroups in structures 1 and 2 are �15.3 and �17.4 kcal/mol,respectively. These intermolecular contacts are considerably lessstabilized compared with the one involving anchored branches.A reasonable explanation for these remarkably different calcu-lated stabilities is that the interaction energy between chargedistributions (48) in a molecular complex lacking directivefunctional groups seems to depend on the van der Waals areainvolved into intermolecular contact. The area of the intermo-lecular overlap of the second-generation branches is apparentlylarger than that of the �-stacked pairs involving naphthalene andp-nitrophenyl rings. Therefore, the interaction between comple-mentary branches in crystal is favorable not only due to itscompactness resulting in the efficient space-filling. It is alsobeneficial from the energetic standpoint.

Consequently, on the basis of the consistent experimental andtheoretical results we reasoned that introduction of second-

Fig. 3. Schematic representation of the intermolecular interaction betweenthe complementary branches. This is reproducibly observed in packing of thesecond generation sulfonimide dendrimers in crystals. Packing of molecularpairs in crystal of compounds 5a (Top), 5b (Middle), and 5c (Bottom).

Fig. 4. Packing of molecular pairs in crystal of compounds 5a (Top), 5b(Middle), and 5c (Bottom).

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generation arylsulfonyl groups that are not supportive of therepeatedly observed interaction depicted in Fig. 3, should changethe packing in crystal. For example, analysis of molecular modelsof compounds 5f and 5g bearing 4-bromobiphenylsulfonyl andmesitylsulfonyl peripheral groups, respectively, shows that theoverlap of second-generation branches in these compoundsshould be highly unfavorable, if not impossible. It is expectedthat in compound 5f the 4-bromobiphenyl units would stick farout of the branch-to-branch contact under study and lead toopen arrangements in the crystal. The resulting voids would,however, be too small to be filled by some solvent molecules tocompensate for the cohesion energy loss. In case of compound5g, the interaction under study is impossible merely because ofits sterically loaded second-generation branches. According tothe model calculations, the o-methyl groups of the peripheralmesitylsulfonyl units should lead to significant changes in theconformation of the corresponding sulfonimide branching pointchanging at least one Car-S-N-S torsion angle from its equilib-rium value of 90° (41) to �150°.

In line with the expectations, crystallization and the subse-quent single-crystal X-ray analysis of compounds 5f and 5grevealed that their packing in crystal does not involve the overlapof the complementary branches, as depicted in Fig. 3, repeatedly

Fig. 5. Packingof5d in crystal (Top), andX-raymolecular structure (Middle) andpacking in crystal of 5e (Bottom). The dotted circle denotes the characteristicintermolecular interaction of the complementary branches (see also Fig. 3).

Fig. 6. Packing of the molecular pair of 6a in crystal (Top), packing of themolecular pair of 6b in crystal (Middle), and a fragment of the crystal packingof 6b viewed along the crystallographic c axis (Bottom). CHCl3 moleculesresiding in the channels are omitted for clarity.

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observed in the 9 above discussed structures. Fig. 7 shows thatalthough the X-ray molecular structure of the compound 5f isvery similar to those of 5a–5d, its molecules pack in crystal inparallel stacks, which are in turn complementary to each other.The resulting structure is dense: It does not contain voids, andno solvent is present in the crystal. The calculated interactionenergy of the X-ray revealed molecule-molecule contact of 2superposed 5f is �49.3 kcal/mol. This value of the interactionenergy is significantly lower than the value of �22.0 kcal/molcalculated for the visionary branch-branch contact involving 2molecules of 5f. Similarly to the above discussed case of thedifferent calculated stabilities of the branch-branch interactionand the �-stacking of naphthalene rings, this is seemingly due toa considerably increased van der Waals area of the intermolec-ular contact in 5f compared with that of the repeatedly observedbranch-branch contact (Fig. 3). Summarizing this tendency, thestructures lacking strong directive functionalities (e.g., hydro-gen-bonding centers) tend to maximize the area of mutualoverlap in molecular pairing.

In accord with the model considerations, X-ray molecularstructure of 5g (Fig. 8 Top Left) has 2 conformationally distortedsulfonimide branching points. This makes the commonly ob-served packing mode (Fig. 3) physically inadmissible. As illus-trated in Fig. 8, the packing of 5g in crystal generates voidsoccupied by CH2Cl2 solvent molecules. Although the packing of5f and 5g in crystal could not be predicted on the basis of bothavailable crystal structures of other second-generation dendriticsulfonimides and theoretical calculations, one can reliably cal-culate the molecular structure and conclude on the feasibility ofthe packing modes.

Finally, the n-octyl chains present in all of the structures understudy do not seem to play any critical role in determining thepacking in crystal. The chains exhibited significant disorder inmost of the presented X-ray structures. The intermolecularcontacts involving the aliphatic chains and aromatic rings re-vealed negligible calculated stabilization energies (�2.0 to �3.0kcal/mol) compared with those of the above discussed intermo-lecular interactions.

ConclusionsIn stark contrast to the vast majority of dendritic molecules thathave low or no tendency to crystallize dendritic oligosulfonim-ides have the advantageous ability to form single crystals with noregard to the peripheral substitution. This allowed carrying outthe unprecedented correlation of molecular and crystal struc-tures of flexible dendritic species. The conclusions drawn in thiscontribution rest upon single-crystal X-ray analyses of 13 den-dritic sulfonimides with systematically modified molecular ar-chitecture and accompanied by theoretical calculations. Thecompounds showed reproducible and tunable packing modes inthe crystalline state. An unlimited structural diversity of den-dritic oligosulfonimides (41–43) makes them highly promisingflexible building blocks for crystal engineering. Properly shapedand functionalized dendritic sulfonimides could possibly be usedin topochemistry and the rational design of materials, such asconducting organic crystals (51, 52). Our approach to thediversity of dendrimer crystals can be equally applied to othertypes of branched compounds, providing their molecular struc-tures can be tailored in a systematic way. We are now focusing

Fig. 7. X-ray molecular structure of 5f (Upper) and a fragment of the crystalpacking of 5f (Bottom).

Fig. 8. Compound 5g: X-ray molecular structure (Upper Left), packing of themolecular pair (Upper Right), and a fragment of the crystal packing viewedalong the crystallographic c axis (Lower). CH2Cl2 molecules residing in thechannels are rendered space-filled.

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on crystallization of larger generation dendrimers and thegrowing of dendrimer cocrystals.

Materials and MethodsThe synthesis of the compounds discussed in this work was either reportedin refs. 41– 43 or carried out following the published methods. Detailedsynthetic procedures and characterization data for new compounds are in

the SI. Single-crystal X-ray analyses were performed on an Xcalibur PX CCDdiffractometer. The details of the crystallographic data and summary ofdata collection and refinement for the dendritic sulfonimides are alsogiven in the SI.

ACKNOWLEDGMENTS. We thank Dr. J. van Heijst (ETH Zurich) for his criticalremarks on the manuscript.

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