Supramolecular Synthons: Validation and Ranking of IntermolecularInteraction EnergiesPublished as part of the Crystal Growth & Design virtual special issue In Honor of Prof. G. R. Desiraju.

J. D. Dunitz*, and A. Gavezzotti*,

Chemistry Department OCL, ETH-Honggerberg, HCI H333, Zurich, SwitzerlandDipartimento di Chimica, University of Milano, Milano, Italy

*S Supporting Information

ABSTRACT: Building upon Desirajus concept of a supramolecularsynthon, we have calculated cohesive energies and thermal stabilities ofmolecular systems related to the proposed synthons. The methodemployed is PIXEL, which allows reliable and extensive mapping ofintermolecular surfaces. Comparisons with accurate ab initio calculationsare included. Stability is judged in terms of calculated binding energies andstretching vibrational amplitudes around room temperature. The list of systems treated includes carboxylic acids, amides,alcohols, NHN hydrogen bonds, as well as benzene stacking and several types of CHO interactions. ClCl synthons arecompared with CHCl synthons. The result is a working table of absolute and relative strengths that could serve as a guidelinefor crystal engineering.

In 1995 Gautam Desiraju introduced the term supra-molecular synthon into the organic crystal chemistryliterature.1 With the concept of the crystal as a supramolecularentity,2 Coreys terminology in synthetic organic chemistrycould be modied to apply to the analysis and design of crystalstructures in terms of functional groups as a basis for theplanning and preparation of new crystals with desiredproperties. Desiraju wrote: Thus supramolecular synthons arestructural units within supermolecules which can be formed and/orassembled by known or conceivable synthetic operations involvingintermolecular interactions.Whatever questions may be raised about this denitiona

list of representative supramolecular synthons is given inDesirajus paperthe notion of the supramolecular synthonhas stuck. It spread rapidly through the crystallographiccommunity to designate a fragmental unit within a moleculethat might lead to a particular intermolecular cohesion mode.Together with supramolecular synthon came Desirajusrevival and extension of the term crystal engineering, rstapplied by G. M. J. Schmidt to the design and control ofphotochemical dimerization reactions in the solid state.3 In thehands of Desiraju and his followers, these terms and conceptshave spurred a remarkable resurgence of interest in organiccrystal chemistry and solid-state reactivity, with far-reachinginuence on the advancement of topics such as opticalmaterials, industrial crystallization, pigments, drug bioavail-ability, and polymorph screeningto mention just a few.4The present Communication provides a quantitative

evaluationwithin the limits of the applied methodologyofthe energy of formation of various molecular dimers classiedas supramolecular synthons (Schemes 13). There is anobvious advantage in attaching an energy tag to a given

supramolecular synthon, especially whenas is commonly thecaseseveral supramolecular synthons coexist in a crystal of acomplex organic compound. Moreover, the same supra-molecular synthon can change its relative importance, depend-ing on substitution.Although typical supramolecular synthons are not exclusively

dimers, we restrict ourselves here to a theoretical study of thiskind of molecular association. Experimental studies ofdimerization energies are scarce, requiring sophisticatedtechniques in the gas phase5 or being aected by environmentaleects in the liquid or solid phases. This is an ideal eld forcomputational theory, and indeed, there is a vast literature onthe calculation of gas-phase dimerization energies by ab initiomethods.614 Although theoretical energy calculations forisolated dimers do not include the inuence of the polarizingeld from other molecules in a crystal environment, this seemsa price worth paying in order to have a set of accurate,transferable, and comparable energy values. We shall have aword to say about the existence of what might be calledantagonist synthonsintermolecular pairings associated withrepulsionand also of what might be called neutral synthons,that is, molecular pairings that provide neither signicantattraction nor repulsion, since both types do appear in actualcrystals.15

Intermolecular energies have been evaluated systematicallyby the PIXEL method,16 which has been shown to mimicclosely the results of higher-level quantum chemical calculationsat a fraction of the computational cost.17 Although the absolute

Received: September 6, 2012Revised: October 16, 2012Published: October 29, 2012

Communication

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2012 American Chemical Society 5873 dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 58735877

values of PIXEL energies may vary by a few percent from thebest available quantum chemical calculations, comparisons ofenergies of related systems should be reliable. Besides, thePIXEL method is well suited for the study of the relativeimportance of dierent aggregation modes in crystals, and itsthousand-fold reduction in computing times with respect tohigh level ab initio allows the study of larger molecules and aneasy calculation of thousands of lattice energies.1517 A furtherbonus of PIXEL is its chemical avor in delivering separateCoulombic, polarization, and dispersion contributions. Inparticular, PIXEL-derived Coulombic and London dispersionterms are very close to the best available theoretical estimates.17

For a selection of supramolecular synthons included in theoriginal paper,1 plus some related systems, a model wasconstructed with standard intramolecular bond distances andangles. Methyl, triuoromethyl, or phenyl groups were attachedat dangling bonds. Although we have restricted the selectionhere to dimeric synthons, extension to higher aggregates issurely possible without serious complications. The systems

chosen to simulate the supramolecular synthon approach areshown in Schemes 1 (strongly hydrogen bonded dimers 118),2 (weakly bonded dimers 1926), and 3 (dimers 2730involving halogen atoms). For each dimer a potential energycurve was constructed by varying in steps some key atomatomdistance to estimate the minimum energy distance, R0. Thecorresponding energy at the minimum, E0 (

of the minimum. Two pseudoforce constants are then dened,as kleft = 10/(R0 Rmin)2 and kright = 10/(R0 Rmax)2 kJ mol12. The average pseudoharmonic force constant is thendened as kav = (kleft + kright)/2, and the anharmonicity index askleft/kright, equal to 1 for a harmonic oscillator, >1 for ananharmonic vibration, and tending to innity as E0 approaches5 kJ mol1. This analysis is obviously inapplicable to energycurves that do not show a minimum. The complete geometries,potential energy curves, and energy decompositions intoCoulombic, polarization, dispersion, and repulsion componentsfor the minimum-energy congurations of all the dimersconsidered here have been deposited as Supporting Informa-tion. (This ensures reproducibility of the results and allows theanalyses to be repeated at any desired value of nRT).Some perspective on theoretical methodologies is needed

here. In high level quantum chemical calculations, for any givenmolecular dimer, the intermolecular stabilization energy isobtained as a dierence between two enormous energiestheenergy of the dimer is only a few millihartree while the energiesof the separate monomers are of the order of a kilohartree. Thecalculation of accurate intermolecular energies by ab initioquantum chemical methods, therefore, demands complex,computationally expensive calculations, especially for disper-sion-dominated organic molecular complexes, such as thosediscussed here. An important advance is the introduction ofdispersion corrections to the relatively aordable densityfunctional theory (DFT) approach.7 During the last ve yearsor so, systematic evaluations of these energies have been carriedout using benchmark ensembles of molecular congurationsfor which top-level values are available,6,9,12a and against whichany proposed computational scheme can be gauged forreliability and cost-eectiveness.12b,14 Previous comparisons16,17

have shown that PIXEL reproduces rather well the ab initioresults at the same level of theory (MP2/6-31G**) as that usedto obtain the electron density: moreover, Table 1 shows somecomparisons with results of benchmark calculations at the topab initio level for some of the dimers considered here. Thecomparison is encouraging, especially when one considers thatbenchmark values refer to fully optimized geometries. Thedisagreement for stacked benzene seems large in percent, but itis small in absolute terms and hardly merits detailed discussion,considering that PIXEL calculations for the benzene dimerspresent in the crystal8 reproduce the lattice energy reasonably

well. We note that PIXEL calculates a repulsive Coulombiccontribution of about 3 kJ mol1 for the stacked benzene dimer.The results of the calculations shown in Tables 2 and 3 more

or less speak for themselves, and we may add merely a fewcomments. As expected, the average force constants decreaseand the anharmonicities increase with decreasing bindingenergy. In this respect, intermolecular cohesion behaves in thesame way as normal intramolecular covalent bonds. One might

Scheme 2 Table 1. Comparison of Energy Results for Some TypicalDimers

dimer benchmarka PIXEL

methanol 24.1 22phenol 29.5 25acetic acid 79.9 72acetamide 68.0 60benzene stacked 11.8 6benzene T-shaped 12.0 11

aFrom the S66 set, ref 12b (for phenol, S22 set, ref 12a).

Table 2. Variable Parameter, Equilibrium Distance (),Binding Energy (kJ mol1), Average Pseudo-harmonic ForceConstant (kJ mol1 2), Anharmonicity Index, andMaximum Stretching Distance () for the Potential EnergyCurves of Hydrogen-Bonded Synthons 118 (Scheme 1)a

synthon,Scheme 1(ref 1) chem descriptn R0 E0 kav

kleft/kright Rmax

1 (1) acetic acid doubleOHO

1.80 72 800 1.0 1.90

2 triuoroacetic aciddouble OHO

1.78 67 550 1.8 1.94

3 (2) acetic acid singleOHO

1.78 32 250 1.0 1.97

4 acetic acid OH...O(plus CHO)

1.88 38 250 4.0 2.20

5 (3) acetamide doubleNHO

1.92 60 425 2.8 2.12

6 (4) acetamide singleNHO

1.96 28 155 4.2 2.40

7 (3) benzamide doubleNHO

1.91 62 680 1.6 2.05

8 benzamide singleNHO

1.95 27 140 3.8 2.30

9 acetic acid/acetamideOHO (plusNHO)

1.92 63 500 1.0 2.06

10 id., acetic acid/triuoroacetamide

1.92 64 350 0.8 2.08

11 id., triuoroaceticacid/acetamide

1.92 62 450 1.3 2.08

12 id., triuoroaceticacid/triuoroacetamide

1.92 60 380 1.1 2.09

13 (6) pyrazole double bentNHN

2.16 58 390 1.8 2.35

14 pyrazole single linearNHN

1.95 39 200 1.6 2.20

15 (28) methanol OHO 1.95 22 130 3.3 2.3716 (28) phenol OHO 1.90 25 130 3.3 2.3017 (18) urea/acetone

bifurcated NHO2.07 37 250 1.0 2.30

18 (18) urea/hexauoroacetonebifurcated NHO

2.13 17 170 7.5 2.65

aSee text for denitions.

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think of dening threshold values for these three bindingdescriptors, but we do not intend to take on this task, whichseems more suitable as an exercise for an InternationalCommission. The stability of a supramolecular synthon,which determines its role and reproducibility in the aggregationprocess, depends in the rst place on the binding energy, butalso on its resistance to thermal uctuation, as represented bythe force constant and hence by the width of the stretchingamplitude Rmax R0.Our analysis serves to provide quantitative expression to a

few important facts. It comes as no surprise that the strongestsupramolecular synthons are held together by OHO, NHN, and NHO hydrogen bonds, in the following order:carboxylic acid OHO pyrazole NHN > carboxylicamides NHO > alcohols OHO with binding energies ofabout 35, 30, and 25 kJ mol1, respectively.18 Acentrosymmetric pair of hydrogen bonds doubles the bindingenergy, except for pyrazole (synthon 13), where geometricrestriction prevents linearity of the NHO grouping in thedimer and thus weakens the strength of the bonds. Thehydrogen bonded synthons in Scheme 1 have binding energiesin the range 70 to 20 kJ mol1 and stretching forceconstants in the range 800 to 130 kJ mol1 2, to be comparedwith typical values of around 400 kJ mol1 and 2000 kJ mol12 for strong covalent bonds. For a mixed supramolecularsynthon, such as the acetic acid/acetamide dimer (synthon 9),the binding energy is closely the sum of the individualhydrogen bond energies. For the strongest synthons, stretchingvibrations are almost harmonic with anharmonicity index kleft/kright less than 2 and a stretching R0 Rmax of 0.20.3 . Forsynthons linked by a single bonding interaction, these valuesincrease up to kleft/kright around 4 and R0 Rmax around 0.4 .Such energy considerations complement the analysis ofcompetitive hydrogen bonding based on structural andchemical properties as well as geometric data retrieved fromcrystallographic databases.19

The nature of the substituent seems to have only a smallinuence on the binding energy, as seen by comparison of theresults for synthons 912 or 1516. However, the electroniccharacter of substituents may change the strength of thesynthon. Thus, replacement of the methyl groups of acetone byelectron withdrawing triuoromethyl groups reduces the energyof the bifurcated hydrogen bond from 37 kJ mol1 in synthon17 to only 17 kJ mol1 in synthon 18. A similar reduction inbinding energy is seen in synthon 2, where the methyl groupsof the acetic acid dimer have been replaced by triuoromethyl.Our calculations draw a clear distinction between traditional

hydrogen bonds (Scheme 1) and other types of interaction(Scheme 2). For example, the double NOCl conformationof synthon 23 provides less than 10 kJ mol1 stabilization, andthe same holds for the various kinds of CHO approaches

shown in Scheme 2, some of which have been classied as weakhydrogen bonds. For synthons that contain both strong andweak hydrogen bonds, such as the acetic acid synthon 3,additivity seems to work; thus, binding energies from individualOHO and CHO interactions yield 32 6.5 = 38.5kJ mol1, almost the same as the calculated value. Some ofthese weaker synthons show strongly anharmonic behavior, andRmax R0 values reach as much as 1.0 (synthons 23 and 25),not far from eective dissociation. According to ourcalculations, cyclic synthon 22 formed by cyano and chlorogroups is unstable, due to CNCN and ClCl repulsiveinteractions. Perhaps this structure should be removed from thelist of supramolecular synthons: otherwise, it represents anexample of an antagonist synthon. For the benzene/hexauorobenzene stacked dimer (synthon 25), our calcu-lations give a binding energy 17 kJ mol1, not far from that ofsome hydrogen-bonding interactions.Although only the linear ClCl system appears in

Desirajus list, close contacts with this and various othergeometries between chlorine atoms in crystals have often beeninterpreted as indications of specic cohesive interactions,rather than as mere consequences of close packing require-ments.20 Scheme 3 shows the systems that we have used in

seeking clarication, and Table 4 gives the results of our PIXELcalculations. The arrangement of two chlorobenzene moleculeswith a linear ClCl arrangement (synthon 27) is only onthe verge of stability (E0 = 2.4 kJ mol1). This marginalstabilization arises, however, not from ClCl interaction butrather from long-range dispersive interaction between thephenyl groups, since the calculated energy of the methylchloride dimer in the same linear arrangement is virtually null.21

Activation by peruoro substitution on the phenyl group(synthon 28) produces only a marginal increase in stability(Table 4). In any case, synthons 27 and 28 are only barelycohesive and qualify merely as neutral synthons. A largerstabilization results for the ClH interaction in synthon 29;besides the more favorable Coulombic interaction, the smallersize of the hydrogen atom allows a larger dispersion

Table 3. As in Table 2, for Weaker Synthons 1926 (Scheme 2)

synthon Scheme 2 (ref 1) chem descriptn, dist consid R0 E0 kav kleft/kright Rmax

19 (7) but-1-en-3-one trans, double CHO 2.40 14 75 2.8 2.920 (8) but-1-en-3-one cis, double CHO 2.35 9 90 8.0 3.121 acetic acid, double CHO 2.35 13 70 3.7 2.9522 (13) double CNCl23 (11) 1-chloro-2-nitropropene double NOCl 3.25 9 60 11.0 4.224 (34) benzene oset stacked vertical interplanar dist 3.7 6 innity25 benzene/hexauorobenzene oset stacked 3.5 17 100 5.3 4.126 (33) benzene T-shaped CH distance bet ring centers 4.8 11 90 10 5.6

Scheme 3

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contribution between the phenyl groups. The binding energy isalmost doubled in synthon 30 with two such ClH contacts.The PIXEL energy dissection into Coulombic and dispersiveenergies (Table 4) clearly supports these interpretations. Adetailed study of general halogen bonding by PIXEL and abinitio methods is available.16

The concept of the supramolecular synthon arose frompattern recognition in crystal structures: the crystal engineerbreaks apart an actual or hypothetical crystal structure in muchthe same way as the organic chemist recognizes precursors in aproposed synthesis of a target molecule. This was the analogybehind Desirajus insight. Our energy calculations conrm that,in most cases, Desirajus synthons correspond to stable crystalbuilding blocks. However, the complexity of the organicmolecular structure is often baing, and obvious problemshamper a straightforward application of the synthon concept:the list of synthons is not exhaustive; crystal structures can bebroken down in many ways; and often many almost equi-energetic crystal structures (polymorphs) are possible for agiven compound. These problems have been recognized anddiscussed over the years both by theoreticians and byexperimentalists. In particular, for crystals involving weakerinteractions, many of our calculated energy surfaces are quiteat, so that the exact geometry of the synthon may be quitevariable and a one-coordinate description in terms of a singleatomatom bond is inappropriate.Our numerical results may suer minor changes with better

computational approaches, but the main message implied in therankings should certainly survive. We hope thereby to haveprovided improvements toward better application of thesupramolecular synthon concept in crystal engineering.

ASSOCIATED CONTENT*S Supporting InformationAtomic coordinates for the minimum-energy congurations ofall the dimers; gures with complete potential energy curvesand graphic representation of each synthon; and table withseparate energy contributions from PIXEL. This material isavailable free of charge via the Internet at http://pubs.acs.org.The PIXEL software with source codes and instruction manualis available for distribution at http://users.unimi.it/gavezzot.

AUTHOR INFORMATIONCorresponding Author*E-mail addresses: J.D.D., dunitz@org.chem.ethz.ch; A.G.,angelo.gavezzotti@unimi.it.

NotesThe authors declare no competing nancial interest.

REFERENCES(1) Desiraju, G. R. Angew. Chem., Int. Ed. 1995, 34, 231.(2) Dunitz, J. D. Thoughts on Crystals as Supermolecules. In The

Crystal as a Supramolecular Entity; Desiraju, G. R., Ed.; John Wiley &Sons: 1996.(3) Schmidt, G. M. J. Pure Appl. Chem. 1971, 27, 647.(4) Moulton, B.; Zaworotko, M. J. Chem. Rev. 2001, 101, 1629.Evans, O. R.; Lin, W. Acc. Chem. Res. 2002, 35, 511.(5) See for example: Alonso, J. L.; Antolinez, S.; Blanco, S.; Lesarri,A.; Lopez, J. C.; Caminati, W. J. Am. Chem. Soc. 2004, 126, 3244.(6) Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 415.(7) Grimme, S. J. Comput. Chem. 2006, 27, 1787.(8) Schweizer, W. B.; Dunitz, J. D. J. Chem. Theory Comput. 2006, 2,288.(9) Pitonak, M.; Hesselmann, A. J. Chem. Theory Comput. 2010, 6,168.(10) Kannemann, F. O.; Becke, A. D. J. Chem. Theory Comput. 2010,

6, 1081.(11) Goerigk, L.; Grimme, S. J. Chem. Theory Comput. 2010, 6, 107.(12) (a) Set S22: Jurecka, P.; Sponer, J.; Cerny, J.; Hobza, P. Phys.

Chem. Chem. Phys. 2006, 8, 1985. (b) Set S66: Rezac, J.; Riley, K. E.;Hobza, P. J. Chem. Theory Comput. 2011, 7, 2427. (c) Riley, K. E.;Pitonak, M.; Cerny, J.; Hobza, P. J. Chem. Theory Comput. 2010, 6, 66.(13) Thanthiriwatte, K. S.; Hohenstein, E. G.; Burns, L. A.; Sherril, C.D. J. Chem. Theory Comput. 2011, 7, 88.(14) Carter, D. J.; Rohl, A. D. J. Chem. Theory Comput. 2012, 8, 281.(15) Gavezzotti, A. Acta Crystallogr. 2010, B66, 396.(16) Gavezzotti, A. Mol. Phys. 2008, 106, 1473.(17) Maschio, L.; Civalleri, B.; Ugliengo, P.; Gavezzotti, A. J. Phys.

Chem. A2011, 115, 11179.(18) There are, of course, many more molecular coupling modes thatqualify as synthons, e.g. the 60-year old, base-pair, WatsonCrickproto-synthon systems, the strength of which exceeds that of thesystems considered here. For another example, the binding energy ofthe glycine zwitterion dimer, arising from the charge-assisted hydrogenbond between the ammonium and carboxylate groups, is of the orderof 95 kJ mol1: Dunitz, J. D.; Gavezzotti, A. J. Phys. Chem. 2012,B116, 6740. Such systems have harmonic stretching behavior within2RT with maximum displacements of the order 0.1 or less.(19) Galek, P. T. A.; Fabian, L.; Motherwell, W. D. S.; Allen, F. H.;Feeder, N. Acta Crystallogr. 2007, B63, 768.(20) Awwadi, F. F.; Willett, R. D.; Peterson, K. A.; Twamley, B.

Chem.Eur. J. 2006, 12, 8952.(21) Gavezzotti, A. J. Chem. Theory Comput. 2005, 1, 834.

Table 4. Results for Synthons Involving Chlorine Atoms(Scheme 3)a

synthon

chemdescriptn,dist consid R0

dist betring

midpts E0Coulombic

termdispersnterm

27 linearClCl

3.55 9.8 2.4 +0.7 5.3

28 activatedlinearClCl

3.55 9.8 3.1 +0.2 5.3

29 linear,singleCHCl

2.5 8.1 5.0 1.2 11.7

30 lateraldoubleCHCl

2.7 7.5 9.1 4.7 18.4

aUnits of and kJ mol1 as in Tables 2 and 3.

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dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 587358775877