Communication pubs.acs.org/crystal
Supramolecular Synthons: Validation and Ranking of Intermolecular Interaction Energies Published 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-Hönggerberg, HCI H333, Zurich, Switzerland Dipartimento di Chimica, University of Milano, Milano, Italy
‡
S Supporting Information *
ABSTRACT: Building upon Desiraju’s concept of a supramolecular synthon, we have calculated cohesive energies and thermal stabilities of molecular systems related to the proposed synthons. The method employed is PIXEL, which allows reliable and extensive mapping of intermolecular surfaces. Comparisons with accurate ab initio calculations are included. Stability is judged in terms of calculated binding energies and stretching vibrational amplitudes around room temperature. The list of systems treated includes carboxylic acids, amides, alcohols, N−H···N hydrogen bonds, as well as benzene stacking and several types of C−H···O interactions. Cl···Cl synthons are compared with C−H···Cl synthons. The result is a working table of absolute and relative strengths that could serve as a guideline for crystal engineering. n 1995 Gautam Desiraju introduced the term “supramolecular synthon” into the organic crystal chemistry literature.1 With the concept of the crystal as a supramolecular entity,2 Corey’s terminology in synthetic organic chemistry could be modified to apply to the analysis and design of crystal structures in terms of functional groups as a basis for the planning and preparation of new crystals with desired properties. Desiraju wrote: “Thus supramolecular synthons are structural units within supermolecules which can be formed and/or assembled by known or conceivable synthetic operations involving intermolecular interactions.” Whatever questions may be raised about this definitiona list of representative supramolecular synthons is given in Desiraju’s paperthe notion of the supramolecular synthon has stuck. It spread rapidly through the crystallographic community to designate a fragmental unit within a molecule that might lead to a particular intermolecular cohesion mode. Together with “supramolecular synthon” came Desiraju’s revival and extension of the term “crystal engineering”, first applied by G. M. J. Schmidt to the design and control of photochemical dimerization reactions in the solid state.3 In the hands of Desiraju and his followers, these terms and concepts have spurred a remarkable resurgence of interest in organic crystal chemistry and solid-state reactivity, with far-reaching influence on the advancement of topics such as optical materials, industrial crystallization, pigments, drug bioavailability, and polymorph screeningto mention just a few.4 The present Communication provides a quantitative evaluationwithin the limits of the applied methodologyof the energy of formation of various molecular dimers classified as supramolecular synthons (Schemes 1−3). There is an obvious advantage in attaching an energy tag to a given
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© 2012 American Chemical Society
supramolecular synthon, especially whenas is commonly the caseseveral supramolecular synthons coexist in a crystal of a complex organic compound. Moreover, the same supramolecular synthon can change its relative importance, depending on substitution. Although typical supramolecular synthons are not exclusively dimers, we restrict ourselves here to a theoretical study of this kind of molecular association. Experimental studies of dimerization energies are scarce, requiring sophisticated techniques in the gas phase5 or being affected by environmental effects in the liquid or solid phases. This is an ideal field for computational theory, and indeed, there is a vast literature on the calculation of gas-phase dimerization energies by ab initio methods.6−14 Although theoretical energy calculations for isolated dimers do not include the influence of the polarizing field from other molecules in a crystal environment, this seems a price worth paying in order to have a set of accurate, transferable, and comparable energy values. We shall have a word to say about the existence of what might be called “antagonist synthons”intermolecular pairings associated with repulsionand also of what might be called “neutral synthons”, that is, molecular pairings that provide neither significant attraction nor repulsion, since both types do appear in actual crystals.15 Intermolecular energies have been evaluated systematically by the PIXEL method,16 which has been shown to mimic closely the results of higher-level quantum chemical calculations at a fraction of the computational cost.17 Although the absolute Received: September 6, 2012 Revised: October 16, 2012 Published: October 29, 2012 5873
dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 5873−5877
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Scheme 1
values of PIXEL energies may vary by a few percent from the best available quantum chemical calculations, comparisons of energies of related systems should be reliable. Besides, the PIXEL method is well suited for the study of the relative importance of different aggregation modes in crystals, and its thousand-fold reduction in computing times with respect to high level ab initio allows the study of larger molecules and an easy calculation of thousands of lattice energies.15−17 A further bonus of PIXEL is its chemical flavor in delivering separate Coulombic, polarization, and dispersion contributions. In particular, PIXEL-derived Coulombic and London dispersion terms are very close to the best available theoretical estimates.17 For a selection of supramolecular synthons included in the original paper,1 plus some related systems, a model was constructed with standard intramolecular bond distances and angles. Methyl, trifluoromethyl, or phenyl groups were attached at dangling bonds. Although we have restricted the selection here to dimeric synthons, extension to higher aggregates is surely possible without serious complications. The systems
chosen to simulate the supramolecular synthon approach are shown in Schemes 1 (strongly hydrogen bonded dimers 1−18), 2 (weakly bonded dimers 19−26), and 3 (dimers 27−30 involving halogen atoms). For each dimer a potential energy curve was constructed by varying in steps some key atom−atom distance to estimate the minimum energy distance, R0. The corresponding energy at the minimum, E0 (1 for an anharmonic vibration, and tending to infinity as E0 approaches −5 kJ mol−1. This analysis is obviously inapplicable to energy curves that do not show a minimum. The complete geometries, potential energy curves, and energy decompositions into Coulombic, polarization, dispersion, and repulsion components for the minimum-energy configurations of all the dimers considered here have been deposited as Supporting Information. (This ensures reproducibility of the results and allows the analyses 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 given molecular dimer, the intermolecular stabilization energy is obtained as a difference between two enormous energiesthe energy of the dimer is only a few millihartree while the energies of the separate monomers are of the order of a kilohartree. The calculation of accurate intermolecular energies by ab initio quantum chemical methods, therefore, demands complex, computationally expensive calculations, especially for dispersion-dominated organic molecular complexes, such as those discussed here. An important advance is the introduction of dispersion corrections to the relatively affordable density functional theory (DFT) approach.7 During the last five years or so, systematic evaluations of these energies have been carried out using “benchmark” ensembles of molecular configurations for which top-level values are available,6,9,12a and against which any proposed computational scheme can be gauged for reliability and cost-effectiveness.12b,14 Previous comparisons16,17 have shown that PIXEL reproduces rather well the ab initio results at the same level of theory (MP2/6-31G**) as that used to obtain the electron density: moreover, Table 1 shows some comparisons with results of benchmark calculations at the top ab initio level for some of the dimers considered here. The comparison is encouraging, especially when one considers that benchmark values refer to fully optimized geometries. The disagreement for stacked benzene seems large in percent, but it is small in absolute terms and hardly merits detailed discussion, considering that PIXEL calculations for the benzene dimers present in the crystal8 reproduce the lattice energy reasonably
Table 2. Variable Parameter, Equilibrium Distance (Å), Binding Energy (kJ mol−1), Average Pseudo-harmonic Force Constant (kJ mol−1 Å−2), Anharmonicity Index, and Maximum Stretching Distance (Å) for the Potential Energy Curves of Hydrogen-Bonded Synthons 1−18 (Scheme 1)a synthon, Scheme 1 (ref 1) 1 (1) 2 3 (2) 4 5 (3) 6 (4) 7 (3) 8 9 10 11 12 13 (6) 14 15 (28) 16 (28) 17 (18) 18 (18)
a
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chem descriptn
R0
E0
kav
kleft/ kright
Rmax
acetic acid double OH···O trifluoroacetic acid double OH···O acetic acid single OH···O acetic acid OH...O (plus CH···O) acetamide double NH···O acetamide single NH···O benzamide double NH···O benzamide single NH···O acetic acid/acetamide OH···O (plus NH···O) id., acetic acid/ trifluoroacetamide id., trifluoroacetic acid/acetamide id., trifluoroacetic acid/ trifluoroacetamide pyrazole double bent NH···N pyrazole single linear N−H···N methanol OH···O phenol OH···O urea/acetone bifurcated NH···O urea/ hexafluoroacetone bifurcated NH···O
1.80
−72
800
1.0
1.90
1.78
−67
550
1.8
1.94
1.78
−32
250
1.0
1.97
1.88
−38
250
4.0
2.20
1.92
−60
425
2.8
2.12
1.96
−28
155
4.2
2.40
1.91
−62
680
1.6
2.05
1.95
−27
140
3.8
2.30
1.92
−63
500
1.0
2.06
1.92
−64
350
0.8
2.08
1.92
−62
450
1.3
2.08
1.92
−60
380
1.1
2.09
2.16
−58
390
1.8
2.35
1.95
−39
200
1.6
2.20
1.95 1.90 2.07
−22 −25 −37
130 130 250
3.3 3.3 1.0
2.37 2.30 2.30
2.13
−17
170
7.5
2.65
See text for definitions. dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 5873−5877
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Communication
Table 3. As in Table 2, for Weaker Synthons 19−26 (Scheme 2) synthon Scheme 2 (ref 1) 19 20 21 22 23 24 25 26
(7) (8) (13) (11) (34) (33)
chem descriptn, dist consid
R0
E0
kav
but-1-en-3-one trans, double CH···O but-1-en-3-one cis, double CH···O acetic acid, double CH···O double CN···Cl 1-chloro-2-nitropropene double NO···Cl benzene offset stacked π···π vertical interplanar dist benzene/hexafluorobenzene offset stacked benzene T-shaped C−H···π distance bet ring centers
2.40 2.35 2.35
−14 −9 −13
75 90 70
2.8 8.0 3.7
2.9 3.1 2.95
3.25 3.7 3.5 4.8
−9 −6 −17 −11
60
11.0 infinity 5.3 10
4.2
100 90
kleft/kright
Rmax
4.1 5.6
shown in Scheme 2, some of which have been classified as weak hydrogen bonds. For synthons that contain both strong and weak hydrogen bonds, such as the acetic acid synthon 3, additivity seems to work; thus, binding energies from individual O−H···O and C−H···O interactions yield −32 − 6.5 = −38.5 kJ mol−1, almost the same as the calculated value. Some of these weaker synthons show strongly anharmonic behavior, and Rmax − R0 values reach as much as 1.0 Å (synthons 23 and 25), not far from effective dissociation. According to our calculations, cyclic synthon 22 formed by cyano and chloro groups is unstable, due to CN···CN and Cl···Cl repulsive interactions. Perhaps this structure should be removed from the list of supramolecular synthons: otherwise, it represents an example of an antagonist synthon. For the benzene/ hexafluorobenzene stacked dimer (synthon 25), our calculations give a binding energy −17 kJ mol−1, not far from that of some hydrogen-bonding interactions. Although only the linear −Cl···Cl system appears in Desiraju’s list, close contacts with this and various other geometries between chlorine atoms in crystals have often been interpreted as indications of specific cohesive interactions, rather than as mere consequences of close packing requirements.20 Scheme 3 shows the systems that we have used in
think of defining threshold values for these three binding descriptors, but we do not intend to take on this task, which seems more suitable as an exercise for an International Commission. The stability of a supramolecular synthon, which determines its role and reproducibility in the aggregation process, depends in the first place on the binding energy, but also on its resistance to thermal fluctuation, as represented by the force constant and hence by the width of the stretching amplitude Rmax − R0. Our analysis serves to provide quantitative expression to a few important facts. It comes as no surprise that the strongest supramolecular synthons are held together by O−H···O, N− H···N, and N−H···O hydrogen bonds, in the following order: carboxylic acid O−H···O ≈ pyrazole N−H···N > carboxylic amides N−H···O > alcohols O−H···O with binding energies of about −35, −30, and −25 kJ mol−1, respectively.18 A centrosymmetric pair of hydrogen bonds doubles the binding energy, except for pyrazole (synthon 13), where geometric restriction prevents linearity of the N−H···O grouping in the dimer and thus weakens the strength of the bonds. The hydrogen bonded synthons in Scheme 1 have binding energies in the range −70 to −20 kJ mol−1 and stretching force constants in the range 800 to 130 kJ mol−1 Å−2, to be compared with typical values of around −400 kJ mol−1 and 2000 kJ mol−1 Å−2 for strong covalent bonds. For a mixed supramolecular synthon, such as the acetic acid/acetamide dimer (synthon 9), the binding energy is closely the sum of the individual hydrogen bond energies. For the strongest synthons, stretching vibrations are almost harmonic with anharmonicity index kleft/ kright less than 2 and a stretching R0 − Rmax of 0.2−0.3 Å. For synthons linked by a single bonding interaction, these values increase up to kleft/kright around 4 and R0 − Rmax around 0.4 Å. Such energy considerations complement the analysis of competitive hydrogen bonding based on structural and chemical properties as well as geometric data retrieved from crystallographic databases.19 The nature of the substituent seems to have only a small influence on the binding energy, as seen by comparison of the results for synthons 9−12 or 15−16. However, the electronic character of substituents may change the strength of the synthon. Thus, replacement of the methyl groups of acetone by electron withdrawing trifluoromethyl groups reduces the energy of the bifurcated hydrogen bond from −37 kJ mol−1 in synthon 17 to only −17 kJ mol−1 in synthon 18. A similar reduction in binding energy is seen in synthon 2, where the methyl groups of the acetic acid dimer have been replaced by trifluoromethyl. Our calculations draw a clear distinction between traditional hydrogen bonds (Scheme 1) and other types of interaction (Scheme 2). For example, the double NO···Cl conformation of synthon 23 provides less than 10 kJ mol−1 stabilization, and the same holds for the various kinds of C−H···O approaches
Scheme 3
seeking clarification, and Table 4 gives the results of our PIXEL calculations. The arrangement of two chlorobenzene molecules with a linear −Cl···Cl− arrangement (synthon 27) is only on the verge of stability (E0 = −2.4 kJ mol−1). This marginal stabilization arises, however, not from Cl···Cl interaction but rather from long-range dispersive interaction between the phenyl groups, since the calculated energy of the methyl chloride dimer in the same linear arrangement is virtually null.21 Activation by perfluoro 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 barely cohesive and qualify merely as neutral synthons. A larger stabilization results for the −Cl···H− interaction in synthon 29; besides the more favorable Coulombic interaction, the smaller size of the hydrogen atom allows a larger dispersion 5876
dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 5873−5877
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Notes
Table 4. Results for Synthons Involving Chlorine Atoms (Scheme 3)a synthon 27 28 29 30 a
chem descriptn, dist consid linear Cl···Cl activated linear Cl···Cl linear, single CH···Cl lateral double CH···Cl
R0
dist bet ring midpts
3.55
9.8
3.55
E0
Coulombic term
dispersn term
−2.4
+0.7
−5.3
9.8
−3.1
+0.2
−5.3
2.5
8.1
−5.0
−1.2
−11.7
2.7
7.5
−9.1
−4.7
−18.4
The authors declare no competing financial interest.
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Units of Å and kJ mol−1 as in Tables 2 and 3.
contribution between the phenyl groups. The binding energy is almost doubled in synthon 30 with two such Cl···H contacts. The PIXEL energy dissection into Coulombic and dispersive energies (Table 4) clearly supports these interpretations. A detailed study of general halogen bonding by PIXEL and ab initio methods is available.16 The concept of the supramolecular synthon arose from pattern recognition in crystal structures: the crystal engineer breaks apart an actual or hypothetical crystal structure in much the same way as the organic chemist recognizes precursors in a proposed synthesis of a target molecule. This was the analogy behind Desiraju’s insight. Our energy calculations confirm that, in most cases, Desiraju’s synthons correspond to stable crystal building blocks. However, the complexity of the organic molecular structure is often baffling, and obvious problems hamper a straightforward application of the synthon concept: the list of synthons is not exhaustive; crystal structures can be broken down in many ways; and often many almost equienergetic crystal structures (polymorphs) are possible for a given compound. These problems have been recognized and discussed over the years both by theoreticians and by experimentalists. In particular, for crystals involving weaker interactions, many of our calculated energy surfaces are quite flat, so that the exact geometry of the synthon may be quite variable and a one-coordinate description in terms of a single atom−atom bond is inappropriate. Our numerical results may suffer minor changes with better computational approaches, but the main message implied in the rankings should certainly survive. We hope thereby to have provided improvements toward better application of the supramolecular synthon concept in crystal engineering.
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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 that qualify as synthons, e.g. the 60-year old, base-pair, Watson−Crick proto-synthon systems, the strength of which exceeds that of the systems considered here. For another example, the binding energy of the glycine zwitterion dimer, arising from the charge-assisted hydrogen bond between the ammonium and carboxylate groups, is of the order of −95 kJ mol−1: Dunitz, J. D.; Gavezzotti, A. J. Phys. Chem. 2012, B116, 6740. Such systems have harmonic stretching behavior within 2RT with maximum displacements of the order 0.1 Å 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.
ASSOCIATED CONTENT
S Supporting Information *
Atomic coordinates for the minimum-energy configurations of all the dimers; figures with complete potential energy curves and graphic representation of each synthon; and table with separate energy contributions from PIXEL. This material is available free of charge via the Internet at http://pubs.acs.org. The PIXEL software with source codes and instruction manual is available for distribution at http://users.unimi.it/gavezzot.
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AUTHOR INFORMATION
Corresponding Author
*E-mail addresses: J.D.D.,
[email protected]; A.G.,
[email protected]. 5877
dx.doi.org/10.1021/cg301293r | Cryst. Growth Des. 2012, 12, 5873−5877
